@article{RosenblumAbelKurthsetal.1999, author = {Rosenblum, Michael and Abel, Hans-Henning and Kurths, J{\"u}rgen and Sch{\"a}fer, Carsten}, title = {Synchronization in the human cardiorespiratory system}, year = {1999}, language = {en} } @article{ParkRosenblumKurthsetal.1999, author = {Park, Eun Hyoung and Rosenblum, Michael and Kurths, J{\"u}rgen and Zaks, Michael A.}, title = {Alternating locking ratios in imperfect phase synchronization}, year = {1999}, language = {en} } @article{HeuerSchultheissHodgsonetal.1999, author = {Heuer, Axel and Schultheiss, J. and Hodgson, N. and Kurths, J{\"u}rgen and Menzel, Ralf and Raab, Volker}, title = {Transverse effects in phase conjugate laser mirrors based on stimulated brillouin scattering}, year = {1999}, language = {en} } @article{SchwarzSpahnGrebogietal.1999, author = {Schwarz, Udo and Spahn, Frank and Grebogi, Celso and Kurths, J{\"u}rgen and Petzschmann, Olaf}, title = {Length scales of clustering in granular gases}, year = {1999}, 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} } @unpublished{PikovskijZaksFeudeletal.1995, author = {Pikovskij, Arkadij and Zaks, Michael A. and Feudel, Ulrike and Kurths, J{\"u}rgen}, title = {Singular continuous spectra in dissipative dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13787}, year = {1995}, abstract = {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 Poincar{\´e} map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincar{\´e} 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.}, language = {en} } @article{RosenblumPikovskijKurths2004, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Synchronization approach to analysis of biological systems}, issn = {0219-4775}, year = {2004}, abstract = {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}, language = {en} } @article{RosenblumKurthsPikovskij2001, author = {Rosenblum, Michael and Kurths, J{\"u}rgen and Pikovskij, Arkadij}, title = {Comment on "Phase synchronization in discrete chaotic systems"}, year = {2001}, abstract = {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.}, language = {en} }