TY  - JOUR
A1  - Frasca, Mattia
A1  - Bergner, Andre
A1  - Kurths, Jürgen
A1  - Fortuna, Luigi
T1  - Bifurcations in a star-like network of Stuart-Landau oscillators
JF  - International journal of bifurcation and chaos : in applied sciences and engineering
N2  - In this paper, we analytically study a star motif of Stuart-Landau oscillators, derive the bifurcation diagram and discuss the different forms of synchronization arising in such a system. Despite the parameter mismatch between the central node and the peripheral ones, an analytical approach independent of the number of units in the system has been proposed. The approach allows to calculate the separatrices between the regions with distinct dynamical behavior and to determine the nature of the different transitions to synchronization appearing in the system. The theoretical analysis is supported by numerical results.
KW  - Complex networks
KW  - synchronization
KW  - bifurcations
Y1  - 2012
U6  - https://doi.org/10.1142/S0218127412501738
SN  - 0218-1274
VL  - 22
IS  - 7
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Malik, Nishant
A1  - Zou, Y.
A1  - Marwan, Norbert
A1  - Kurths, Jürgen
T1  - Dynamical regimes and transitions in plio-pleistocene Asian monsoon
JF  - epl : a letters journal exploring the frontiers of physics
N2  - We propose a novel approach based on the fluctuation of similarity to identify regimes of distinct dynamical complexity in short time series. A statistical test is developed to estimate the significance of the identified transitions. Our method is verified by uncovering bifurcation structures in several paradigmatic models, providing more complex transitions compared with traditional Lyapunov exponents. In a real-world situation, we apply this method to identify millennial-scale dynamical transitions in Plio-Pleistocene proxy records of the South Asian summer monsoon system. We infer that many of these transitions are induced by the external forcing of the solar insolation and are also affected by internal forcing on Monsoonal dynamics, i.e., the glaciation cycles of the Northern Hemisphere and the onset of the Walker circulation.
Y1  - 2012
U6  - https://doi.org/10.1209/0295-5075/97/40009
SN  - 0295-5075
VL  - 97
IS  - 4
PB  - EDP Sciences
CY  - Mulhouse
ER  - 
TY  - JOUR
A1  - Huang, Tingwen
A1  - Chen, Guanrong
A1  - Kurths, Jürgen
T1  - Synchronization of chaotic of chaotic systems with time-varying coupöing delays
JF  - Discrete and continuous dynamical systems : a journal bridging mathematics and sciences ; Series B, Mathematical modelling, analysis and computations
N2  - In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation in equalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method.
KW  - Synchronization
KW  - Chaotic System
KW  - Time-varying Delay
Y1  - 2011
U6  - https://doi.org/10.3934/dcdsb.2011.16.1071
SN  - 1531-3492
VL  - 16
IS  - 4
SP  - 1071
EP  - 1082
PB  - American Institute of Mathematical Sciences
CY  - Springfield
ER  - 
TY  - JOUR
A1  - Koseska, Aneta
A1  - Volkov, Evgenii
A1  - Kurths, Jürgen
T1  - Synthetic multicellular oscillatory systems controlling protein dynamics with genetic circuits
JF  - Physica scripta : an international journal for experimental and theoretical physics
N2  - Synthetic biology is a relatively new research discipline that combines standard biology approaches with the constructive nature of engineering. Thus, recent efforts in the field of synthetic biology have given a perspective to consider cells as 'programmable matter'. Here, we address the possibility of using synthetic circuits to control protein dynamics. In particular, we show how intercellular communication and stochasticity can be used to manipulate the dynamical behavior of a population of coupled synthetic units and, in this manner, finely tune the expression of specific proteins of interest, e.g. in large bioreactors.
Y1  - 2011
U6  - https://doi.org/10.1088/0031-8949/84/04/045007
SN  - 0031-8949
VL  - 84
IS  - 4
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Rusconi, Marco
A1  - Valleriani, Angelo
A1  - Dunlop, John William Chapman
A1  - Kurths, Jürgen
A1  - Weinkamer, Richard
T1  - Quantitative approach to the stochastics of bone remodeling
JF  - epl : a letters journal exploring the frontiers of physics
N2  - During life bones constantly adapt their structure to their mechanical environment via a mechanically controlled process called bone remodeling. For trabecular bone, this process modifies the thickness of each trabecula leading occasionally to full resorption. We describe the irreversible dynamics of the trabecular thickness distribution (TTD) by means of a Markov chain discrete in space and time. By using thickness data from adult patients, we derive the transition probabilities in the chain. This allows a quantification, in terms of geometrical quantities, of the control of bone remodeling and thus to determine the evolution of the TTD with age.
Y1  - 2012
U6  - https://doi.org/10.1209/0295-5075/97/28009
SN  - 0295-5075
VL  - 97
IS  - 2
PB  - EDP Sciences
CY  - Mulhouse
ER  - 
TY  - JOUR
A1  - Gandhimathi, V. M.
A1  - Rajasekar, S.
A1  - Kurths, Jürgen
T1  - Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators
JF  - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics
N2  - We study the overdamped version of two coupled anharmonic oscillators under the influence of both low- and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented. (c) 2006 Elsevier B.V. All rights reserved.
KW  - vibrational resonance
KW  - low-frequency force
KW  - high-frequency force
KW  - stochastic resonance
KW  - noise
KW  - mean residence time
Y1  - 2006
U6  - https://doi.org/10.1016/j.physleta.2006.08.051
SN  - 0375-9601
VL  - 360
IS  - 2
SP  - 279
EP  - 286
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Zou, Yong
A1  - Thiel, M.
A1  - Romano, Maria Carmen
A1  - Kurths, Jürgen
A1  - Bi, Q.
T1  - Shrimp structure and associated dynamics in parametrically excited oscillators
JF  - International journal of bifurcation and chaos : in applied sciences and engineering
N2  - We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system.
KW  - bifurcation analysis
KW  - recurrence plot
KW  - period doubling
KW  - intermittency
Y1  - 2006
U6  - https://doi.org/10.1142/S0218127406016987
SN  - 0218-1274
VL  - 16
IS  - 12
SP  - 3567
EP  - 3579
PB  - World Scientific Publ. Co
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Zhou, Changsong
A1  - Zemanova, Lucia
A1  - Zamora, Gorka
A1  - Hilgetag, Claus C.
A1  - Kurths, Jürgen
T1  - Hierarchical organization unveiled by functional connectivity in complex brain networks
JF  - Physical review letters
N2  - How do diverse dynamical patterns arise from the topology of complex networks? We study synchronization dynamics in the cortical brain network of the cat, which displays a hierarchically clustered organization, by modeling each node (cortical area) with a subnetwork of interacting excitable neurons. We find that in the biologically plausible regime the dynamics exhibits a hierarchical modular organization, in particular, revealing functional clusters coinciding with the anatomical communities at different scales. Our results provide insights into the relationship between network topology and functional organization of complex brain networks.
Y1  - 2006
U6  - https://doi.org/10.1103/PhysRevLett.97.238103
SN  - 0031-9007
SN  - 1079-7114
VL  - 97
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Kopitzki, K.
A1  - Warnke, P. C.
A1  - Saparin, Peter
A1  - Kurths, Jürgen
A1  - Timmer, Jens
T1  - Comment on "Kullback-Leibler and renormalized entropies: Applications to electroencephalograms of epilepsy patients"
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Zhang, H.
A1  - Hu, B.
A1  - Hu, G.
A1  - Ouyang, Q.
A1  - Kurths, Jürgen
T1  - Turbulence control by developing a spiral wave with a periodic signal injection in the complex Ginzburg-Laundau equation
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
T1  - Noise-induced phase synchronization and synchronization transitions in chaotic oscillators
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Tokuda, I.
A1  - Kurths, Jürgen
A1  - Rosa, Epaminondas
T1  - Learning phase synchronization from nonsynchronized chaotic regimes
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Kuznetsov, A. S.
A1  - Kurths, Jürgen
T1  - Stable heteroclinic cycles for ensembles of chaotic oscillators
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Raab, Corinna
A1  - Kurths, Jürgen
T1  - Estimation of Large-Scale Dimension Densities
N2  - We propose a technique to calculate large-scale dimension densities in both higher-dimensional spatio-temporal systems and low-dimensional systems from only a few data points, where known methods usually have an unsatisfactory scaling behavior. This is mainly due to boundary and finite size effects. With our rather simple method we normalize boundary effects and get a significant correction of the dimension estimate. This straightforward approach is basing on rather general assumptions. So even weak coherent structures obtained from small spatial couplings can be detected with this method, what is impossible by using the Lyapunov-dimension density. We demonstrate the efficiency of our technique for coupled logistic maps, coupled tent maps, the Lorenz-attractor and the Roessler-attractor.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - Murali, K.
A1  - Kurths, Jürgen
T1  - Simple electronic circuit model for doubly stochastic resonance
N2  - We have recently reported the phenomenon of doubly stochastic resonance [Phys. Rev. Lett. 85, 227 (2000)], a synthesis of noise-induced transition and stochastic resonance. The essential feature of this phenomenon is that multiplicative noise induces a bimodality and additive noise causes stochastic resonance behavior in the induced structure. In the present paper we outline possible applications of this effect and design a simple lattice of electronic circuits for the experimental realization of doubly stochastic resonance.
Y1  - 2001
UR  - http://link.aps.org/abstract/PRE/v63/e020103
ER  - 
TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - Kurths, Jürgen
T1  - Additive noise in noise-induced nonequilibrium transitions
Y1  - 2001
SN  - 1054-1500
ER  - 
TY  - JOUR
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
A1  - Hu, B.
T1  - Array-enhanced coherence resonance: Nontrivial effects of heterogeneity and spatial independence of noise
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Hassan, M. K.
A1  - Kurths, Jürgen
T1  - Transition from random to ordered fractals in fragmentation of particles in an open system
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Hassan, M. K.
A1  - Kurths, Jürgen
T1  - Competitive random sequential adsorption of point and fixed-sized particles: analytical results
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Zöller, Gert
A1  - Hainzl, Sebastian
A1  - Kurths, Jürgen
T1  - Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Gowin, W.
A1  - Saparin, Peter
A1  - Kurths, Jürgen
A1  - Felsenberg, D.
T1  - Bone Architecture assessment with Measures of Complexity
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Gowin, W.
A1  - Saparin, Peter
A1  - Kurths, Jürgen
T1  - Bone architecture quantification: Measures of complexity compared to failure lead results
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Anishchenko, Vadim S.
A1  - Vadivasova, T. E.
A1  - Kopeikin, A. S.
A1  - Kurths, Jürgen
A1  - Strelkova, G. I.
T1  - Effect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Wessel, Niels
A1  - Voss, Andreas
A1  - Kurths, Jürgen
A1  - Schirdewan, Alexander
A1  - Hnatkova, Katarina
A1  - Malik, Marek
T1  - Evaluation of renormalised entropy for risk stratification using heart rate variability data
N2  - Standard time and frequency parameters of heart rate variability (HRV) describe only linear and periodic behaviour, whereas more complex relationships cannot be recognised. A method that may be capable of assessing more complex properties is the non-linear measure of 'renormalised entropy.' A new concept of the method, RE(AR), has been developed, based on a non-linear renormalisation of autoregressive spectral distributions. To test the hypothesis that renormalised entropy may improve the result of high-risk stratification after myocardial infarction, it is applied to a clinical pilot study (41 subjects) and to prospective data of the St George's Hospital post- infarction database (572 patients). The study shows that the new RE(AR) method is more reproducible and more stable in time than a previously introduced method (p<0.001). Moreover, the results of the study confirm the hypothesis that on average, the survivors have negative values of RE(AR) (-0.11+/-0.18), whereas the non-survivors have positive values (0.03+/-0.22, p<0.01). Further, the study shows that the combination of an HRV triangular index and RE(AR) leads to a better prediction of sudden arrhythmic death than standard measurements of HRV. In summary, the new RE(AR) method is an independent measure in HRV analysis that may be suitable for risk stratification in patients after myocardial infarction.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - Kurths, Jürgen
A1  - Schimansky-Geier, Lutz
T1  - Doubly stochastic resonance
N2  - We report the effect of doubly stochastic resonance which appears in nonlinear extended systems if the influence of noise is twofold: A multiplicative noise induces bimodality of the mean field of the coupled network and an independent additive noise governs the dynamic behavior in response to small periodic driving. For optimally selected values of the additive noise intensity stochastic resonance is observed, which is manifested by a maximal coherence between the dynamics of the mean field and the periodic input. Numerical simulations of the signal-to-noise ratio and theoretical results from an effective two state model are in good quantitative agreement.
Y1  - 2000
UR  - http://link.aps.org/abstract/PRL/v85/p227
ER  - 
TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - Kurths, Jürgen
T1  - Additive noise and noise-induced nonequilibrium phase transitions
Y1  - 2000
SN  - 1-563-96826-6
ER  - 
TY  - JOUR
A1  - Wessel, Niels
A1  - Ziehmann, Christine
A1  - Kurths, Jürgen
A1  - Meyerfeldt, Udo
A1  - Schirdewan, Alexander
A1  - Voss, Andreas
T1  - Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates
N2  - Ventricular tachycardia or fibrillation (VT-VF) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this study is to find early signs of sustained VT-VF in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they store the 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study these 1000 beat-to-beat intervals of 17 chronic heart failure ICD patients before the onset of a life-threatening arrhythmia and at a control time, i.e., without a VT-VF event. To characterize these rather short data sets, we calculate heart rate variability parameters from the time and frequency domain, from symbolic dynamics as well as the finite-time growth rates. We find that neither the time nor the frequency domain parameters show significant differences between the VT-VF and the control time series. However, two parameters from symbolic dynamics as well as the finite-time growth rates discriminate significantly both groups. These findings could be of importance in algorithms for next generation ICD's to improve the diagnostics and therapy of VT-VF.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Landa, Polina S.
A1  - Zaikin, Alexei A.
A1  - Ushakov, V. G.
A1  - Kurths, Jürgen
T1  - Influence of additive noise on transitions in nonlinear systems
N2  - The effect of additive noise on transitions in nonlinear systems far from equilibrium is studied. It is shown that additive noise in itself can induce a hidden phase transition, which is similar to the transition induced by multiplicative noise in a nonlinear oscillator [P. Landa and A. Zaikin, Phys. Rev. E 54, 3535 (1996)]. Investigation of different nonlinear models that demonstrate phase transitions induced by multiplicative noise shows that the influence of additive noise upon such phase transitions can be crucial: additive noise can either blur such a transition or stabilize noise-induced oscillations.
Y1  - 2000
UR  - http://link.aps.org/abstract/PRE/v61/p4809
ER  - 
TY  - JOUR
A1  - Landa, Polina S.
A1  - Zaikin, Alexei A
A1  - Kurths, Jürgen
T1  - On noise-induced transitions in nonlinear oscillators
Y1  - 2000
SN  - 3-540- 41074-0
ER  - 
TY  - JOUR
A1  - Wessel, Niels
A1  - Schumann, Agnes
A1  - Wessel, Niels
A1  - Schumann, Agnes
A1  - Schirdewan, Alexander
A1  - Voss, Andreas
A1  - Kurths, Jürgen
T1  - Entropy measures in heart rate variability data
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Wessel, Niels
A1  - Voss, Andreas
A1  - Malberg, Hagen
A1  - Ziehmann, Christine
A1  - Voss, Henning U.
A1  - Schirdewan, Alexander
A1  - Meyerfeldt, Udo
A1  - Kurths, Jürgen
T1  - Nonlinear analysis of complex phenomena in cardiological data
N2  - The main intention of this contribution is to discuss different nonlinear approaches to heart rate and blood pressure variability analysis for a better understanding of the cardiovascular regulation. We investigate measures of complexity which are based on symbolic dynamics, renormalised entropy and the finite time growth rates. The dual sequence method to estimate the baroreflex sensitivity and the maximal correlation method to estimate the nonlinear coupling between time series are employed for analysing bivariate data. The latter appears to be a suitable method to estimate the strength of the nonlinear coupling and the coupling direction. Heart rate and blood pressure data from clinical pilot studies and from very large clinical studies are analysed. We demonstrate that parameters from nonlinear dynamics are useful for risk stratification after myocardial infarction, for the prediction of life-threatening cardiac events even in short time series, and for modelling the relationship between heart rate and blood pressure regulation. These findings could be of importance for clinical diagnostics, in algorithms for risk stratification, and for therapeutic and preventive tools of next generation implantable cardioverter defibrillators.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Kurths, Jürgen
A1  - Zschau, Jochen
T1  - Seismic quiescence as an indicator for large earthquakes in a system of self-organized criticality
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Anishchenko, Vadim S.
A1  - Kopeikin, A. S.
A1  - Kurths, Jürgen
T1  - Studying hyperbolicity in chaotic systems
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Ziehmann, Christine
A1  - Smith, Leonard A.
A1  - Kurths, Jürgen
T1  - Localized Lyapunov exponents and the prediction of predictability
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Boccaletti, Stefano
A1  - Valladares, D. L.
A1  - Kurths, Jürgen
T1  - Synchronization of chaotic structurally nonequivalent systems
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Kurths, Jürgen
T1  - Self-organization of spatio-temporal earthquake clusters
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Park, Eun Hyoung
A1  - Kurths, Jürgen
T1  - On phase synchronization by periodic force in chaotic oscillators with saddle equilibria
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Kurths, Jürgen
T1  - Self-organized criticality model for earthquakes : Quiescence, foreshocks and aftershocks
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Lai, Ying Cheng
A1  - Grebogi, Celso
A1  - Kurths, Jürgen
T1  - Modeling of deterministic chaotic systems
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Park, Eun Hyoung
A1  - Zaks, Michael A.
A1  - Kurths, Jürgen
T1  - Phase synchronization in the forced lorenz system
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Kurths, Jürgen
T1  - Similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Voss, Henning U.
A1  - Kurths, Jürgen
T1  - Reconstruction of nonlinear time-delayed feedback models from optical data
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Ziehmann, Christine
A1  - Smith, L.
A1  - Kurths, Jürgen
T1  - The bootstrap and lyapunov exponents in deterministic chaos
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Zaikin, Alexei A.
A1  - Kurths, Jürgen
T1  - Modeling Cognitive Control in Simple Movements
Y1  - 1999
SN  - 1-563-96863-0
ER  - 
TY  - JOUR
A1  - Kolodner, P.
A1  - Abel, Markus
A1  - Kurths, Jürgen
A1  - Voss, Henning U.
T1  - Amplitude equations from spatiotemporal binary-fluid convection data
Y1  - 1999
UR  - http://www.stat.physik.uni-potsdam.de/~markus/papers/PRL83-3422.pdf
ER  - 
TY  - JOUR
A1  - Schwache, A.
A1  - Kurths, Jürgen
A1  - Mitschke, F.
A1  - Voss, Henning U.
T1  - Equations of motion from chaotic data : a driven optical fiber ring resonator
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Braun, Robert
A1  - Feudel, Fred
A1  - Gebogi, C.
A1  - Kurths, Jürgen
A1  - Witt, Annette
T1  - Tracer dynamics in a flow of driven vortices
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Abel, Hans-Henning
A1  - Kurths, Jürgen
A1  - Schäfer, Carsten
T1  - Synchronization in the human cardiorespiratory system
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Park, Eun Hyoung
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
A1  - Zaks, Michael A.
T1  - Alternating locking ratios in imperfect phase synchronization
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Heuer, Axel
A1  - Schultheiss, J.
A1  - Hodgson, N.
A1  - Kurths, Jürgen
A1  - Menzel, Ralf
A1  - Raab, Volker
T1  - Transverse effects in phase conjugate laser mirrors based on stimulated brillouin scattering
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Schwarz, Udo
A1  - Spahn, Frank
A1  - Grebogi, Celso
A1  - Kurths, Jürgen
A1  - Petzschmann, Olaf
T1  - Length scales of clustering in granular gases
Y1  - 1999
ER  - 
TY  - GEN
A1  - Motter, Adilson E.
A1  - Matias, Manuel A.
A1  - Kurths, Jürgen
A1  - Ott, Edward
T1  - Dynamics on complex networks and applications
T2  - Physica. D, Nonlinear phenomena
KW  - complex systems
KW  - nonlinear dynamics
KW  - statistical physics
Y1  - 2006
U6  - https://doi.org/10.1016/j.physd.2006.09.012
SN  - 0167-2789
VL  - 224
IS  - 1-2
SP  - VII
EP  - VIII
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Zemanova, Lucia
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
T1  - Structural and functional clusters of complex brain networks
JF  - Physica, D, Nonlinear phenomena
N2  - Recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. It is of importance to understand the implications of such complex network structures in the functional organization of the brain activities. Here we study this problem from the viewpoint of dynamical complex networks. We investigate synchronization dynamics on the corticocortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behavior, and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.
KW  - cortical network
KW  - anatomical connectivity
KW  - functional connectivity
KW  - topological community
KW  - dynamical cluster
Y1  - 2006
U6  - https://doi.org/10.1016/j.physd.2006.09.008
SN  - 0167-2789
SN  - 1872-8022
VL  - 224
IS  - 1-2
SP  - 202
EP  - 212
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Meucci, Riccardo
A1  - Salvadori, Francesco
A1  - Ivanchenko, Mikhail V.
A1  - Al Naimee, Kais
A1  - Zhou, Chansong
A1  - Arecchi, Fortunato Tito
A1  - Boccaletti, Stefano
A1  - Kurths, Jürgen
T1  - Synchronization of spontaneous bursting in a CO2 laser
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.
Y1  - 2006
U6  - https://doi.org/10.1103/PhysRevE.74.066207
SN  - 2470-0045
SN  - 2470-0053
VL  - 74
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - INPR
A1  - Pikovskij, Arkadij
A1  - Zaks, Michael A.
A1  - Feudel, Ulrike
A1  - Kurths, Jürgen
T1  - Singular continuous spectra in dissipative dynamics
N2  - We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.
T3  - NLD Preprints - 15 
Y1  - 1995
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13787
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Synchronization approach to analysis of biological systems
N2  - In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss the potentials as well as limitations and misinterpretations of the approach
Y1  - 2004
SN  - 0219-4775
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
T1  - Comment on "Phase synchronization in discrete chaotic systems"
N2  - Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Popovych, Orest
A1  - Maistrenko, Yu
A1  - Mosekilde, Erik
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Transcritical riddling in a system of coupled maps
N2  - The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold. In this way, the transcritical riddling bifurcation is substituted by a symmetry-breaking bifurcation, which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state.
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
T1  - Phase synchronization in regular and chaotic systems
Y1  - 2000
SN  - 0218-1274
ER  - 
TY  - BOOK
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
T1  - Synchronization : a universal concept in nonlinear sciences
T3  - Cambridge nonlinear science series
Y1  - 2001
SN  - 0-521-59285-2
VL  - 12
PB  - Cambridge Univ. Press
CY  - Cambridge
ET  - 1st paperback ed., repr
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Zaks, Michael A.
A1  - Kurths, Jürgen
T1  - Phase synchronization of regular and chaotic oscillators
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Popovych, Orest
A1  - Maistrenko, Yu
A1  - Mosekilde, Erik
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Transcritical loss of synchronization in coupled chaotic systems
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - On the generalized dimensions for the fourier spectrum of the thue-morse sequence
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Tass, Peter
A1  - Rosenblum, Michael
A1  - Weule, J.
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
A1  - Volkmann, J.
A1  - Schnitzler, A.
A1  - Freund, H.-J.
T1  - Detection of n:m phase locking from noisy data : application to magnetoencephalography
N2  - We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase difference, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - From Phase to Lag Synchronization in Coupled Chaotic Oscillators
N2  - We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe thisregime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Coherence Resonance in a Noise-Driven Excitable System
N2  - We study the dynamics of the excitable Fitz Hugh-Nagumo system under external noisy driving. Noise activates the system producing a sequence of pulses. The coherence of these noise-induced oscillations is shown to be maximal for a certain noise amplitude. This new effect of coherence resonance is explained by different noise dependencies of the activation and the excursion times. A simple one-dimensional model based on the Langevin dynamics is proposed for the quantitative description of this phenomenon.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
A1  - Schafer, C.
A1  - Tass, Peter
A1  - Abel, Hans-Henning
T1  - Synchronization in Noisy Systems and Cardiorespiratory Interaction
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Ruzick, Oliver
A1  - Scheffczyk, Christian
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Dynamics of chaos-order interface in coupled map lattices
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Symbolic dynamics behind the singular continuous power spectra of continuous flows
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Witt, Annette
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
T1  - Testing stationarity in time series
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase synchronization in noisy and chaotic oscillators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - On the correlation dimension of the spectral measure for the Thue-Morse sequence
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase synchronization in driven and coupled chaotic oscillators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Effect of phase synchronization in driven chaotic oscillators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Coherence resonance in a noise-driven excitable system
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Romano, Maria Carmen
A1  - Thiel, M.
A1  - Kurths, Jürgen
A1  - Kiss, Istvan Z.
A1  - Hudson, J. L.
T1  - Detection of synchronization for non-phase-coherent and non-stationary data
N2  - We present a new method to detect phase as well as generalized synchronization in a wide class of complex systems. It is based on the recurrences of the system's trajectory to the neighborhood of a former state in phase space. We illustrate the applicability of the algorithm for the paradigmatic chaotic Rossler system in the funnel regime and for noisy data, where other methods to detect phase synchronization fail. Furthermore, we demonstrate for electrochemical experiments that the method can easily detect phase and generalized synchronization in non-phase- coherent and even non-stationary time series
Y1  - 2005
SN  - 0295-5075
ER  - 
TY  - JOUR
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
A1  - Kiss, Istvan Z.
A1  - Hudson, J. L.
T1  - Noise-enhanced phase synchronization of chaotic oscillators
Y1  - 2002
ER  - 
TY  - INPR
A1  - Kurths, Jürgen
A1  - Pikovskij, Arkadij
A1  - Scheffczyk, Christian
T1  - Roughening interfaces in deterministic dynamics
N2  - Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.
T3  - NLD Preprints - 3 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13447
ER  - 
TY  - JOUR
A1  - Stolbova, Veronika
A1  - Surovyatkina, Elena
A1  - Bookhagen, Bodo
A1  - Kurths, Jürgen
T1  - Tipping elements of the Indian monsoon: Prediction of onset and
withdrawal
JF  - Geophysical research letters
N2  - Forecasting the onset and withdrawal of the Indian summer monsoon is crucial for the life and prosperity of more than one billion inhabitants of the Indian subcontinent. However, accurate prediction of monsoon timing remains a challenge, despite numerous efforts. Here we present a method for prediction of monsoon timing based on a critical transition precursor. We identify geographic regions-tipping elements of the monsoon-and use them as observation locations for predicting onset and withdrawal dates. Unlike most predictability methods, our approach does not rely on precipitation analysis but on air temperature and relative humidity, which are well represented both in models and observations. The proposed method allows to predict onset 2 weeks earlier and withdrawal dates 1.5 months earlier than existing methods. In addition, it enables to correctly forecast monsoon duration for some anomalous years, often associated with El Nino-Southern Oscillation.
Y1  - 2016
U6  - https://doi.org/10.1002/2016GL068392
SN  - 0094-8276
SN  - 1944-8007
VL  - 43
SP  - 3982
EP  - 3990
PB  - American Geophysical Union
CY  - Washington
ER  - 
TY  - GEN
A1  - Thiel, Marco
A1  - Romano, Maria Carmen
A1  - Kurths, Jürgen
A1  - Rolfs, Martin
T1  - Twin Surrogates to Test for Complex Synchronisation
N2  - We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of R¨ossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems.
T3  - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - paper 264 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57231
ER  - 
TY  - JOUR
A1  - Ivanchenko, Mikhail V.
A1  - Osipov, Grigory V.
A1  - Shalfeev, V. D.
A1  - Kurths, Jürgen
T1  - Phase synchronization in ensembles of bursting oscillators
N2  - We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles
Y1  - 2004
SN  - 0031-9007
ER  - 
TY  - JOUR
A1  - Ivanchenko, Mikhail V.
A1  - Osipov, Grigory V.
A1  - Shalfeev, V. D.
A1  - Kurths, Jürgen
T1  - Phase synchronization of chaotic intermittent oscillations
N2  - We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization
Y1  - 2004
SN  - 0031-9007
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase Synchronization of Chaotic Rotators
N2  - We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor.
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
A1  - Osipov, Grigory V.
A1  - Kiss, Istvan Z.
A1  - Hudson, J. L.
T1  - Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Zaks, Michael A.
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Osipov, Grigory V.
A1  - Kurths, Jürgen
T1  - Phase synchronization of chaotic oscillations in terms of periodic orbits
Y1  - 1997
SN  - 1054-1500
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Osipov, Grigory V.
A1  - Kurths, Jürgen
T1  - Phase synchronization effects in a lattice of nonidentical Rössler oscillators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase synchronization of chaotic oscillators by external driving
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Boccaletti, Stefano
A1  - Kurths, Jürgen
A1  - Osipov, Grigory V.
T1  - The synchronization of chaotic systems
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Kurths, Jürgen
T1  - Regular and chaotic phase synchronization of coupled circle maps
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Zaks, Michael A.
A1  - Kurths, Jürgen
T1  - Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization
N2  - The chaotically driven circle map is considered as the simplest model ofphase synchronization of a chaotic continuous-time oscillator by external periodic force. The phase dynamics is analyzed via phase-locking regions of the periodic cycles embedded in the strange attractor. It is shown that full synchronization, where all the periodic cycles are phase locked, disappears via the attractor-repeller collision. Beyond the transition an intermittent regime with exponentially rare phase slips, resulting from the trajectory's hits on an eyelet, is observed.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Ivanchenko, Mikhail V.
A1  - Osipov, Grigory V.
A1  - Shalfeev, V. D.
A1  - Kurths, Jürgen
T1  - Synchronization of two non-scalar-coupled limit-cycle oscillators
N2  - Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar- coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved
Y1  - 2004
ER  - 
TY  - JOUR
A1  - Belykh, Vladimir N.
A1  - Osipov, Grigory V.
A1  - Kuckländer, Nina
A1  - Blasius, Bernd
A1  - Kurths, Jürgen
T1  - Automatic control of phase synchronization in coupled complex oscillators
N2  - We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic R"ossler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic R"ossler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.
Y1  - 2005
UR  - http://www.agnld.uni-potsdam.de/~bernd/papers/physica_D.pdf
ER  - 
TY  - JOUR
A1  - Kurths, Jürgen
A1  - Romano, Maria Carmen
A1  - Thiel, Marco
A1  - Osipov, Grigory V.
A1  - Ivanchenko, Mikhail V.
A1  - Kiss, Istvan Z.
A1  - Hudson, John L.
T1  - Synchronization analysis of coupled noncoherent oscillators
N2  - We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators
Y1  - 2006
UR  - http://www.springerlink.com/content/102972
U6  - https://doi.org/10.1007/s11071-006-1957-x
SN  - 0924-090X
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Ivanchenko, Mikhail V.
A1  - Kurths, Jürgen
A1  - Hu, B.
T1  - Synchronized chaotic intermittent and spiking behavior in coupled map chains
N2  - We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks
Y1  - 2005
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Maheswaran, Rathinasamy
A1  - Agarwal, Ankit
A1  - Sivakumar, Bellie
A1  - Marwan, Norbert
A1  - Kurths, Jürgen
T1  - Wavelet analysis of precipitation extremes over India and teleconnections to climate indices
JF  - Stochastic Environmental Research and Risk Assessment
N2  - Precipitation patterns and extremes are significantly influenced by various climatic factors and large-scale atmospheric circulation patterns. This study uses wavelet coherence analysis to detect significant interannual and interdecadal oscillations in monthly precipitation extremes across India and their teleconnections to three prominent climate indices, namely, Nino 3.4, Pacific Decadal Oscillation, and Indian Ocean Dipole (IOD). Further, partial wavelet coherence analysis is used to estimate the standalone relationship between the climate indices and precipitation after removing the effect of interdependency. The wavelet analysis of monthly precipitation extremes at 30 different locations across India reveals that (a) interannual (2-8 years) and interdecadal (8-32 years) oscillations are statistically significant, and (b) the oscillations vary in both time and space. The results from the partial wavelet coherence analysis reveal that Nino 3.4 and IOD are the significant drivers of Indian precipitation at interannual and interdecadal scales. Intriguingly, the study also confirms that the strength of influence of large-scale atmospheric circulation patterns on Indian precipitation extremes varies with spatial physiography of the region.
KW  - Extreme precipitation
KW  - Teleconnection patterns
KW  - Wavelets
KW  - Partial wavelet coherence
KW  - India
Y1  - 2019
U6  - https://doi.org/10.1007/s00477-019-01738-3
SN  - 1436-3240
SN  - 1436-3259
VL  - 33
IS  - 11-12
SP  - 2053
EP  - 2069
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Ozturk, Ugur
A1  - Marwan, Norbert
A1  - Korup, Oliver
A1  - Saito, H.
A1  - Agarwa, Ankit
A1  - Grossman, M. J.
A1  - Zaiki, M.
A1  - Kurths, Jürgen
T1  - Complex networks for tracking extreme rainfall during typhoons
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - Reconciling the paths of extreme rainfall with those of typhoons remains difficult despite advanced forecasting techniques. We use complex networks defined by a nonlinear synchronization measure termed event synchronization to track extreme rainfall over the Japanese islands. Directed networks objectively record patterns of heavy rain brought by frontal storms and typhoons but mask out contributions of local convective storms. We propose a radial rank method to show that paths of extreme rainfall in the typhoon season (August-November, ASON) follow the overall southwest-northeast motion of typhoons and mean rainfall gradient of Japan. The associated eye-of-the-typhoon tracks deviate notably and may thus distort estimates of heavy typhoon rainfall. We mainly found that the lower spread of rainfall tracks in ASON may enable better hindcasting than for westerly-fed frontal storms in June and July.
Y1  - 2018
U6  - https://doi.org/10.1063/1.5004480
SN  - 1054-1500
SN  - 1089-7682
VL  - 28
IS  - 7
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Marwan, Norbert
A1  - Nowaczyk, Norbert R.
A1  - Kurths, Jürgen
A1  - Thiel, Marco
T1  - Cross recurrence plot based rescaling of geological time series
N2  - The rescaling of geological data series to a geological reference time series is of major interest in many investigations. For example, geophysical borehole data should be correlated to a given data series whose time scale is known in order to achieve an age-depth function or the sedimentation rate for the borehole data. Usually this synchronization is performed visually and by hand. Instead of using this wiggle matching by eye, we present the application of cross recurrence plots for such tasks. Using this method, the synchronization and rescaling of geological data to a given time scale is much easier and faster than by hand.
Y1  - 2001
SN  - 1029-7006
ER  - 
TY  - JOUR
A1  - Agarwal, Ankit
A1  - Maheswaran, Rathinasamy
A1  - Marwan, Norbert
A1  - Caesar, Levke
A1  - Kurths, Jürgen
T1  - Wavelet-based multiscale similarity measure for complex networks
JF  - The European physical journal : B, Condensed matter and complex systems
N2  - In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson’s correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson’s correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales.
KW  - Statistical and Nonlinear Physics
Y1  - 2018
U6  - https://doi.org/10.1140/epjb/e2018-90460-6
SN  - 1434-6028
SN  - 1434-6036
VL  - 91
IS  - 11
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Kurths, Jürgen
A1  - Agarwal, Ankit
A1  - Shukla, Roopam
A1  - Marwan, Norbert
A1  - Maheswaran, Rathinasamy
A1  - Caesar, Levke
A1  - Krishnan, Raghavan
A1  - Merz, Bruno
T1  - Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach
JF  - Nonlinear processes in geophysics
N2  - A better understanding of precipitation dynamics in the Indian subcontinent is required since India's society depends heavily on reliable monsoon forecasts. We introduce a non-linear, multiscale approach, based on wavelets and event synchronization, for unravelling teleconnection influences on precipitation. We consider those climate patterns with the highest relevance for Indian precipitation. Our results suggest significant influences which are not well captured by only the wavelet coherence analysis, the state-of-the-art method in understanding linkages at multiple timescales. We find substantial variation across India and across timescales. In particular, El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mainly influence precipitation in the south-east at interannual and decadal scales, respectively, whereas the North Atlantic Oscillation (NAO) has a strong connection to precipitation, particularly in the northern regions. The effect of the Pacific Decadal Oscillation (PDO) stretches across the whole country, whereas the Atlantic Multidecadal Oscillation (AMO) influences precipitation particularly in the central arid and semi-arid regions. The proposed method provides a powerful approach for capturing the dynamics of precipitation and, hence, helps improve precipitation forecasting.
Y1  - 2019
U6  - https://doi.org/10.5194/npg-26-251-2019
SN  - 1023-5809
SN  - 1607-7946
VL  - 26
IS  - 3
SP  - 251
EP  - 266
PB  - Copernicus
CY  - Göttingen
ER  - 
TY  - JOUR
A1  - Marwan, Norbert
A1  - Kurths, Jürgen
T1  - Nonlinear analysis of bivariate data with cross recurrence plots
N2  - We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Nino data.
Y1  - 2001
UR  - http://arxiv.org/abs/physics/0201061
ER  -