@article{LandaUshakovKurths2006,
  author    = {Landa, Polina S. and Ushakov, Vladimir and Kurths, J{\"u}rgen},
  title     = {Rigorous theory of stochastic resonance in overdamped bistable oscillators for weak signals},
  series = {Chaos, solitons \& fractals : applications in science and engineering},
  volume    = {30},
  journal   = {Chaos, solitons \& fractals : applications in science and engineering},
  number    = {3},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0960-0779},
  doi       = {10.1016/j.chaos.2005.08.116},
  pages     = {574 -- 578},
  year      = {2006},
  abstract  = {The results of the theoretical consideration of stochastic resonance in overdamped bistable oscillators are given. These results are founded not on the model of two states as in [McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys Rev A 1989;39:4854-69], but on splitting of motion into regular and random and the rigorous solution of the Fokker-Planck equation for the random component. We show that this resonance is caused by a change, under the influence of noise, of the system's effective stiffness and damping factor contained in the equation for the regular component. For a certain value of the noise intensity the effective stiffness is minimal, and this fact causes non-monotonic change of the output signal amplitude as the noise intensity changes. It is important that the location of the minimum and its value depend essentially on the signal frequency.},
  language  = {en}
}
@article{BaptistaZhouKurths2006,
  author    = {Baptista, Murilo da Silva and Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Information transmission in phase synchronous chaotic arrays},
  issn      = {0256-307X},
  doi       = {10.1088/0256-307X/23/3/010},
  year      = {2006},
  abstract  = {We show many versatile phase synchronous configurations that emerge in an array of coupled chaotic elements due to the presence of a periodic stimulus. Then, we explain the relevance of these configurations to the understanding of how information about such a. stimulus is transmitted from one side to the other in this array. The stimulus actively creates the ways to be transmitted, by making the chaotic elements to phase synchronize},
  language  = {en}
}
@article{ChenShiauTsengetal.2010,
  author    = {Chen, Jin-Long and Shiau, Yuo-Hsien and Tseng, Yin-Jiun and Chiu, Hung-Wen and Hsiao, Tzu-Chien and Wessel, Niels and Kurths, J{\"u}rgen and Chu, Woei-Chyn},
  title     = {Concurrent sympathetic activation and vagal withdrawal in hyperthyroidism : evidence from detrended fluctuation analysis of heart rate variability},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2009.12.062},
  year      = {2010},
  abstract  = {Despite many previous Studies on the association between hyperthyroidism and the hyperadrenergic state, controversies still exist. Detrended fluctuation analysis (DFA) is a well recognized method in the nonlinear analysis of heart rate variability (HRV), and it has physiological significance related to the autonomic nervous system. In particular, an increased short-term scaling exponent alpha 1 calculated from DFA is associated with both increased sympathetic activity and decreased vagal activity. No study has investigated the DFA of HRV in hyperthyroidism. This study was designed to assess the sympathovagal balance in hyperthyroidism. We performed the DFA along with the linear analysis of HRV in 36 hyperthyroid Graves' disease patients (32 females and 4 males; age 30 +/- 1 years, means +/- SE) and 36 normal controls matched by sex, age and body mass index. Compared with the normal controls, the hyperthyroid patients revealed a significant increase (P < 0.001) in alpha 1 (hyperthyroid 1.28 +/- 0.04 versus control 0.91 +/- 0.02), long-term scaling exponent alpha 2 (1.05 +/- 0.02 versus 0.90 +/- 0.01), overall scaling exponent alpha (1.11 +/- 0.02 versus 0.89 +/- 0.01), low frequency power in normalized units (LF\%) and the ratio of low frequency power to high frequency power (LF/HF); and a significant decrease (P < 0.001) in the standard deviation of the R-R intervals (SDNN) and high frequency power (HF). In conclusion, hyperthyroidism is characterized by concurrent sympathetic activation and vagal withdrawal. This sympathovagal imbalance state in hyperthyroidism helps to explain the higher prevalence of atrial fibrillation and exercise intolerance among hyperthyroid patients.},
  language  = {en}
}
@book{WittNeimanKurths1997,
  author    = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen},
  title     = {Characterizing the dynamics of stochastic bistable systems by measures of complexity},
  series = {Preprint NLD},
  volume    = {36},
  journal   = {Preprint NLD},
  publisher = {Univ. Potsdam},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {20 S. : graph. Darst.},
  year      = {1997},
  language  = {en}
}
@article{SunLuKurthsetal.2009,
  author    = {Sun, Xiaojuan and Lu, Qishao and Kurths, J{\"u}rgen and Wang, Qingyun},
  title     = {Spatiotemporal coherence resonance in a map lattice},
  issn      = {0218-1274},
  doi       = {10.1142/S021812740902310X},
  year      = {2009},
  abstract  = {We study the effects of parametric noise on a lattice network, which is locally modeled by a two-dimensional Rulkov map. We conclude that at some intermediate noise intensity, parametric noise can induce ordered circular patterns, which indicates the appearance of spatiotemporal coherence resonance in the studied lattice. With the observation of coherence-like manner in linear spatial cross-correlation, the coherence phenomena can be analyzed quantitatively.},
  language  = {en}
}
@article{KoseskaVolkovKurths2009,
  author    = {Koseska, Aneta and Volkov, Evgenij and Kurths, J{\"u}rgen},
  title     = {Detuning-dependent dominance of oscillation death in globally coupled synthetic genetic oscillators},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/85/28002},
  year      = {2009},
  abstract  = {We study dynamical regimes of globally coupled genetic relaxation oscillators in the presence of small detuning. Using bifurcation analysis, we find that under strong coupling via the slow variable, the detuning can eliminate standard oscillatory solutions in a large region of the parameter space, providing the dominance of oscillation death. This result is substantially different from previous results on oscillation quenching, where for homogeneous populations, the coexistence of oscillation death and limit cycle oscillations is always present. We propose further that this effect of detuning-dependent dominance could be a powerful regulator of genetic network's dynamics.},
  language  = {en}
}
@article{ZhouKurths2006,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Hierarchical synchronization in complex networks with heterogeneous degrees},
  issn      = {1054-1500},
  doi       = {10.1063/1.2150381},
  year      = {2006},
  abstract  = {We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function. (C) 2006 American Institute of Physics},
  language  = {en}
}
@article{PereiraBaptistaReyesetal.2009,
  author    = {Pereira, Tiago and Baptista, Murilo da Silva and Reyes, Marcelo B. and Caldas, Ibere Luiz and Sartorelli, Jos{\´e} Carlos and Kurths, J{\"u}rgen},
  title     = {A scenario for torus T-2 destruction via a global bifurcation},
  issn      = {0960-0779},
  doi       = {10.1016/j.chaos.2007.06.115},
  year      = {2009},
  abstract  = {We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T-2 with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type- if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws.},
  language  = {en}
}
@article{RusconiVallerianiDunlopetal.2009,
  author    = {Rusconi, Marco and Valleriani, Angelo and Dunlop, John William Chapman and Kurths, J{\"u}rgen and Weinkamer, Richard},
  title     = {Insights into the control of trabecular bone remodelling obtained by a Markov model},
  issn      = {8756-3282},
  doi       = {10.1016/j.bone.2009.03.467},
  year      = {2009},
  language  = {en}
}
@book{KurthsMayerKress1998,
  author    = {Kurths, J{\"u}rgen and Mayer-Kress, Gottfried},
  title     = {Nonlinear analysis of physiological data},
  editor    = {Kantz, Holger},
  publisher = {Springer},
  address   = {Berlin, New York},
  isbn      = {3-540-63481-9},
  pages     = {VIII, 344 S. : Ill., graph. Darst.},
  year      = {1998},
  language  = {en}
}
@article{VossKurths1998,
  author    = {Voss, Henning U. and Kurths, J{\"u}rgen},
  title     = {Test for nonlinear dynamical behavior in symbol sequences},
  year      = {1998},
  language  = {en}
}
@article{VossKurths1997,
  author    = {Voss, Henning U. and Kurths, J{\"u}rgen},
  title     = {Reconstruction of nonlinear time delay models from data by the use of optimal transformations},
  year      = {1997},
  language  = {en}
}
@article{WittNeimanKurths1997,
  author    = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen},
  title     = {Charakterizing the dynamics of stochastic bistable systems by measures of complexity},
  year      = {1997},
  language  = {en}
}
@article{ChenShangZhouetal.2009,
  author    = {Chen, Maoyin and Shang, Yun and Zhou, Changsong and Wu, Ye and Kurths, J{\"u}rgen},
  title     = {Enhanced synchronizability in scale-free networks},
  issn      = {1054-1500},
  doi       = {10.1063/1.3062864},
  year      = {2009},
  abstract  = {We introduce a modified dynamical optimization coupling scheme to enhance the synchronizability in the scale- free networks as well as to keep uniform and converging intensities during the transition to synchronization. Further, the size of networks that can be synchronizable exceeds by several orders of magnitude the size of unweighted networks.},
  language  = {en}
}
@article{SpahnKatzorkePetzschmannetal.1997,
  author    = {Spahn, Frank and Katzorke, Ines and Petzschmann, Olaf and Schwarz, Udo and Kurths, J{\"u}rgen},
  title     = {Cluster instabiliy of granular assemblies},
  year      = {1997},
  language  = {en}
}
@article{SpahnSchwarzKurths1997,
  author    = {Spahn, Frank and Schwarz, Udo and Kurths, J{\"u}rgen},
  title     = {Clustering of granular assemblies with temperature dependent restitution under Keplerian differential rotation},
  year      = {1997},
  language  = {en}
}
@book{RosenblumSchaeferAbeletal.1997,
  author    = {Rosenblum, Michael and Sch{\"a}fer, Carsten and Abel, Hans-Henning and Kurths, J{\"u}rgen},
  title     = {Interrelationship of Parasympathetic Innervation of the Sinoatrial Node and the Atrioventricular Node of Human Heart},
  issn      = {1120-1797},
  year      = {1997},
  language  = {en}
}
@article{SaparinKurthsGowinetal.1997,
  author    = {Saparin, Peter and Kurths, J{\"u}rgen and Gowin, P. and Felsenberg, D.},
  title     = {Die quantitative Beurteilung trabecul{\"a}rer Knochenstrukturen der Lendenwirbelk{\"o}rper durch Meßmethoden der nicht-linearen Dynamik},
  year      = {1997},
  language  = {de}
}
@article{ZaikinRosenblumLandaetal.1997,
  author    = {Zaikin, Alexei A. and Rosenblum, Michael and Landa, Polina S. and Kurths, J{\"u}rgen},
  title     = {Control of noise-induced oscillations of a pendulum with a rondomly vibrating suspension axis},
  year      = {1997},
  language  = {en}
}
@article{WesselKleinerVossetal.1997,
  author    = {Wessel, Niels and Kleiner, H. J. and Voss, Andreas and Kurths, J{\"u}rgen and Dietz, R.},
  title     = {Nonlinear dynamics in cardiovasscular diseases},
  year      = {1997},
  language  = {en}
}
@article{ZaikinRosenblumScheffczyketal.1997,
  author    = {Zaikin, Alexei A. and Rosenblum, Michael and Scheffczyk, Christian and Engbert, Ralf and Krampe, Ralf-Thomas and Kurths, J{\"u}rgen},
  title     = {Modeling qualitative changes in bimanual movements},
  year      = {1997},
  language  = {en}
}
@article{FeudelJansenKurthsetal.1997,
  author    = {Feudel, Ulrike and Jansen, Wolfgang and Kurths, J{\"u}rgen and Schwarz, Udo and Voss, Henning U.},
  title     = {Solar variability : simple models and proxy data},
  isbn      = {4-274-90187-4},
  year      = {1997},
  language  = {en}
}
@article{GowinKurthsSaparinetal.1997,
  author    = {Gowin, W. and Kurths, J{\"u}rgen and Saparin, Peter and Felsenberg, D.},
  title     = {Measures of complexity and processing of vertebral CT-images},
  isbn      = {0-7803-4262-3},
  year      = {1997},
  language  = {en}
}
@article{PereiraBaptistaReyesetal.2006,
  author    = {Pereira, Tiago and Baptista, Murilo da Silva and Reyes, Marcelo Bussotti and Caldas, Ibere Luiz and Sartorelli, Jos{\´e} Carlos and Kurths, J{\"u}rgen},
  title     = {Global bifurcation destroying the experimental torus T-2},
  doi       = {10.1103/Physreve.73.017201},
  year      = {2006},
  abstract  = {We show experimentally the scenario of a two-frequency torus T-2 breakdown, in which a global bifurcation occurs due to the collision of a torus with an unstable periodic orbit, creating a heteroclinic saddle connection, followed by an intermittent behavior},
  language  = {en}
}
@article{WuZhouXiaoetal.2010,
  author    = {Wu, Ye Wu and Zhou, Changsong and Xiao, Jinghua and Kurths, J{\"u}rgen and Schellnhuber, Hans Joachim},
  title     = {Evidence for a bimodal distribution in human communication},
  issn      = {0027-8424},
  doi       = {10.1073/pnas.1013140107},
  year      = {2010},
  abstract  = {Interacting human activities underlie the patterns of many social, technological, and economic phenomena. Here we present clear empirical evidence from Short Message correspondence that observed human actions are the result of the interplay of three basic ingredients: Poisson initiation of tasks and decision making for task execution in individual humans as well as interaction among individuals. This interplay leads to new types of interevent time distribution, neither completely Poisson nor power-law, but a bimodal combination of them. We show that the events can be separated into independent bursts which are generated by frequent mutual interactions in short times following random initiations of communications in longer times by the individuals. We introduce a minimal model of two interacting priority queues incorporating the three basic ingredients which fits well the distributions using the parameters extracted from the empirical data. The model can also embrace a range of realistic social interacting systems such as e-mail and letter communications when taking the time scale of processing into account. Our findings provide insight into various human activities both at the individual and network level. Our analysis and modeling of bimodal activity in human communication from the viewpoint of the interplay between processes of different time scales is likely to shed light on bimodal phenomena in other complex systems, such as interevent times in earthquakes, rainfall, forest fire, and economic systems, etc.},
  language  = {en}
}
@article{ZakharovaVadivasovaAnishchenkoetal.2010,
  author    = {Zakharova, Anna and Vadivasova, Tatjana and Anishchenko, Vadim S. and Koseska, Aneta and Kurths, J{\"u}rgen},
  title     = {Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.81.011106},
  year      = {2010},
  abstract  = {We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.},
  language  = {en}
}
@article{GozolchianiMoshelHausdorffetal.2006,
  author    = {Gozolchiani, Avi and Moshel, Shay and Hausdorff, Jeffrey M. and Simon, Ely and Kurths, J{\"u}rgen and Havlin, Shlomo},
  title     = {Decaying of phase synchronization in parkinsonian tremor},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2005.10.033},
  year      = {2006},
  abstract  = {We describe effects of the asymmetry of cycles and non-stationarity in time series on the phase synchronization method which may lead to artifacts. We develop a modified method that overcomes these effects and apply it to study parkinsonian tremor. Our results indicate that there is synchronization between two different hands and provide information about the time delay separating their dynamics. These findings suggest that this method may be useful for detecting and quantifying weak synchronization between two non-stationary signals.},
  language  = {en}
}
@article{SenthilkumarKurths2010,
  author    = {Senthilkumar, Dharmapuri Vijayan and Kurths, J{\"u}rgen},
  title     = {Characteristics and synchronization of time-delay systems driven by a common noise},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2010-01273-4},
  year      = {2010},
  abstract  = {We investigate the characteristics of time-delay systems in the presence of Gaussian noise. We show that the delay time embedded in the time series of time-delay system with constant delay cannot be estimated in the presence noise for appropriate values of noise intensity thereby forbidding any possibility of phase space reconstruction. We also demonstrate the existence of complete synchronization between two independent identical time-delay systems driven by a common noise without explicitly establishing any external coupling between them.},
  language  = {en}
}
@article{BergnerFrascaSciutoetal.2012,
  author    = {Bergner, Andre and Frasca, M. and Sciuto, G. and Buscarino, A. and Ngamga, Eulalie Joelle and Fortuna, L. and Kurths, J{\"u}rgen},
  title     = {Remote synchronization in star networks},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {85},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.85.026208},
  pages     = {7},
  year      = {2012},
  abstract  = {We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism.},
  language  = {en}
}
@article{ZakharovaKurthsVadivasovaetal.2011,
  author    = {Zakharova, Anna and Kurths, J{\"u}rgen and Vadivasova, Tatyana and Koseska, Aneta},
  title     = {Analysing dynamical behavior of cellular networks via stochastic bifurcations},
  series = {PLoS one},
  volume    = {6},
  journal   = {PLoS one},
  number    = {5},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1932-6203},
  doi       = {10.1371/journal.pone.0019696},
  pages     = {12},
  year      = {2011},
  abstract  = {The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.},
  language  = {en}
}
@article{FrascaBergnerKurthsetal.2012,
  author    = {Frasca, Mattia and Bergner, Andre and Kurths, J{\"u}rgen and Fortuna, Luigi},
  title     = {Bifurcations in a star-like network of Stuart-Landau oscillators},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {22},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {7},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127412501738},
  pages     = {13},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@article{MalikZouMarwanetal.2012,
  author    = {Malik, Nishant and Zou, Y. and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Dynamical regimes and transitions in plio-pleistocene Asian monsoon},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {97},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  number    = {4},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/97/40009},
  pages     = {6},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@article{HuangChenKurths2011,
  author    = {Huang, Tingwen and Chen, Guanrong and Kurths, J{\"u}rgen},
  title     = {Synchronization of chaotic of chaotic systems with time-varying coup{\"o}ing delays},
  series = {Discrete and continuous dynamical systems : a journal bridging mathematics and sciences ; Series B, Mathematical modelling, analysis and computations},
  volume    = {16},
  journal   = {Discrete and continuous dynamical systems : a journal bridging mathematics and sciences ; Series B, Mathematical modelling, analysis and computations},
  number    = {4},
  publisher = {American Institute of Mathematical Sciences},
  address   = {Springfield},
  issn      = {1531-3492},
  doi       = {10.3934/dcdsb.2011.16.1071},
  pages     = {1071 -- 1082},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}
@article{KoseskaVolkovKurths2011,
  author    = {Koseska, Aneta and Volkov, Evgenii and Kurths, J{\"u}rgen},
  title     = {Synthetic multicellular oscillatory systems controlling protein dynamics with genetic circuits},
  series = {Physica scripta : an international journal for experimental and theoretical physics},
  volume    = {84},
  journal   = {Physica scripta : an international journal for experimental and theoretical physics},
  number    = {4},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0031-8949},
  doi       = {10.1088/0031-8949/84/04/045007},
  pages     = {10},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}
@article{RusconiVallerianiDunlopetal.2012,
  author    = {Rusconi, Marco and Valleriani, Angelo and Dunlop, John William Chapman and Kurths, J{\"u}rgen and Weinkamer, Richard},
  title     = {Quantitative approach to the stochastics of bone remodeling},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {97},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  number    = {2},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/97/28009},
  pages     = {6},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@article{GandhimathiRajasekarKurths2006,
  author    = {Gandhimathi, V. M. and Rajasekar, S. and Kurths, J{\"u}rgen},
  title     = {Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators},
  series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  volume    = {360},
  journal   = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  number    = {2},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2006.08.051},
  pages     = {279 -- 286},
  year      = {2006},
  abstract  = {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.},
  language  = {en}
}
@article{ZouThielRomanoetal.2006,
  author    = {Zou, Yong and Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen and Bi, Q.},
  title     = {Shrimp structure and associated dynamics in parametrically excited oscillators},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {16},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {12},
  publisher = {World Scientific Publ. Co},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127406016987},
  pages     = {3567 -- 3579},
  year      = {2006},
  abstract  = {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.},
  language  = {en}
}
@article{ZhouZemanovaZamoraetal.2006,
  author    = {Zhou, Changsong and Zemanova, Lucia and Zamora, Gorka and Hilgetag, Claus C. and Kurths, J{\"u}rgen},
  title     = {Hierarchical organization unveiled by functional connectivity in complex brain networks},
  series = {Physical review letters},
  volume    = {97},
  journal   = {Physical review letters},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.97.238103},
  pages     = {4},
  year      = {2006},
  abstract  = {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.},
  language  = {en}
}
@article{KopitzkiWarnkeSaparinetal.2002,
  author    = {Kopitzki, K. and Warnke, P. C. and Saparin, Peter and Kurths, J{\"u}rgen and Timmer, Jens},
  title     = {Comment on "Kullback-Leibler and renormalized entropies: Applications to electroencephalograms of epilepsy patients"},
  year      = {2002},
  language  = {en}
}
@article{ZhangHuHuetal.2002,
  author    = {Zhang, H. and Hu, B. and Hu, G. and Ouyang, Q. and Kurths, J{\"u}rgen},
  title     = {Turbulence control by developing a spiral wave with a periodic signal injection in the complex Ginzburg-Laundau equation},
  year      = {2002},
  language  = {en}
}
@article{ZhouKurths2002,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Noise-induced phase synchronization and synchronization transitions in chaotic oscillators},
  year      = {2002},
  language  = {en}
}
@article{TokudaKurthsRosa2002,
  author    = {Tokuda, I. and Kurths, J{\"u}rgen and Rosa, Epaminondas},
  title     = {Learning phase synchronization from nonsynchronized chaotic regimes},
  year      = {2002},
  language  = {en}
}
@article{KuznetsovKurths2002,
  author    = {Kuznetsov, A. S. and Kurths, J{\"u}rgen},
  title     = {Stable heteroclinic cycles for ensembles of chaotic oscillators},
  year      = {2002},
  language  = {en}
}
@article{RaabKurths2001,
  author    = {Raab, Corinna and Kurths, J{\"u}rgen},
  title     = {Estimation of Large-Scale Dimension Densities},
  year      = {2001},
  abstract  = {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.},
  language  = {en}
}
@article{ZaikinMuraliKurths2001,
  author    = {Zaikin, Alexei A. and Murali, K. and Kurths, J{\"u}rgen},
  title     = {Simple electronic circuit model for doubly stochastic resonance},
  year      = {2001},
  abstract  = {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.},
  language  = {en}
}
@article{ZaikinKurths2001,
  author    = {Zaikin, Alexei A. and Kurths, J{\"u}rgen},
  title     = {Additive noise in noise-induced nonequilibrium transitions},
  issn      = {1054-1500},
  year      = {2001},
  language  = {en}
}
@article{ZhouKurthsHu2001,
  author    = {Zhou, Changsong and Kurths, J{\"u}rgen and Hu, B.},
  title     = {Array-enhanced coherence resonance: Nontrivial effects of heterogeneity and spatial independence of noise},
  year      = {2001},
  language  = {en}
}
@article{HassanKurths2001,
  author    = {Hassan, M. K. and Kurths, J{\"u}rgen},
  title     = {Transition from random to ordered fractals in fragmentation of particles in an open system},
  year      = {2001},
  language  = {en}
}
@article{HassanKurths2001,
  author    = {Hassan, M. K. and Kurths, J{\"u}rgen},
  title     = {Competitive random sequential adsorption of point and fixed-sized particles: analytical results},
  year      = {2001},
  language  = {en}
}
@article{ZoellerHainzlKurths2001,
  author    = {Z{\"o}ller, Gert and Hainzl, Sebastian and Kurths, J{\"u}rgen},
  title     = {Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes},
  year      = {2001},
  language  = {en}
}