@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{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} } @misc{MotterMatiasKurthsetal.2006, author = {Motter, Adilson E. and Matias, Manuel A. and Kurths, J{\"u}rgen and Ott, Edward}, title = {Dynamics on complex networks and applications}, series = {Physica. D, Nonlinear phenomena}, volume = {224}, journal = {Physica. D, Nonlinear phenomena}, number = {1-2}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-2789}, doi = {10.1016/j.physd.2006.09.012}, pages = {VII -- VIII}, year = {2006}, language = {en} } @article{ZemanovaZhouKurths2006, author = {Zemanova, Lucia and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Structural and functional clusters of complex brain networks}, series = {Physica, D, Nonlinear phenomena}, volume = {224}, journal = {Physica, D, Nonlinear phenomena}, number = {1-2}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-2789}, doi = {10.1016/j.physd.2006.09.008}, pages = {202 -- 212}, year = {2006}, abstract = {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.}, language = {en} } @article{MeucciSalvadoriIvanchenkoetal.2006, author = {Meucci, Riccardo and Salvadori, Francesco and Ivanchenko, Mikhail V. and Al Naimee, Kais and Zhou, Chansong and Arecchi, Fortunato Tito and Boccaletti, Stefano and Kurths, J{\"u}rgen}, title = {Synchronization of spontaneous bursting in a CO2 laser}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {74}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.74.066207}, pages = {6}, year = {2006}, abstract = {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.}, language = {en} } @article{OzturkMarwanKorupetal.2018, author = {Ozturk, Ugur and Marwan, Norbert and Korup, Oliver and Saito, H. and Agarwa, Ankit and Grossman, M. J. and Zaiki, M. and Kurths, J{\"u}rgen}, title = {Complex networks for tracking extreme rainfall during typhoons}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {28}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {7}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5004480}, pages = {8}, year = {2018}, abstract = {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.}, language = {en} } @misc{AllefeldKurths2004, author = {Allefeld, Carsten and Kurths, J{\"u}rgen}, title = {Testing for phase synchronization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-20091}, year = {2004}, abstract = {We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-samples test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series.}, language = {en} } @misc{AllefeldKurths2004, author = {Allefeld, Carsten and Kurths, J{\"u}rgen}, title = {An approach to multivariate phase synchronization analysis and its application to event-related potentials}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-20106}, year = {2004}, abstract = {A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.}, language = {en} }