Synchronization of a periodic oscillator by external force; 4. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. He is a fellow of the American Physical Society and fellow of the Fraunhofer Society Germany , and is currently the chairman for Nonlinear Processes in Geophysics and member of the council in Geophysics of the European Geophysical Society. He obtained his PhD in Physics, and started to work on nonlinear data analysis and chaos in 1984. Classical results for the synchronization of periodic self-sustained oscillations subject to a noisy driving are reviewed and compared with recently found phase synchronization effects in chaotic oscillators. Arkady Pikovsky studied radiophysics and physics at Gorky State University, and started to work on chaos in 1976, describing an electronic device generating chaos in his Diploma thesis and later proving it experimentally. It presents a conductance-based model that includes the M-type K+ conductance, gM, the persistent Na+ conductance, gNaP, and the cationic h conductance, gh.
Synchronization of chaotic systems 6. It should find its place on the shelves of many science libraries because it supplies sufficient resources to both the layperson and the specialist. Synchronization of a periodic oscillator by external force 4. In 2001 he will be a member of the Editorial Board of the Int. Different approaches to the phase definition in chaotic systems, as well as the phase dynamics, are duscussed.
In this study, how the synaptic plasticity influences the collective bursting dynamics in a modular neuronal network is numerically investigated. About the Author: Arkady Pikovsky was part of the Max-Planck research group on nonlinear dynamics, before becoming a professor at the University of Potsdam, Germany. He obtained his PhD in Physics, and started to work on nonlinear data analysis and chaos in 1984. The term synchronization as used here describes how two or more coupled nonlinear oscillators adjust their initially different natural rhythms to a common frequency and constant relative phase. Professor Kurths was director of the group for Nonlinear Dynamics of the Max-Planck Society from 1992-1996.
In this brief review, starting with a derivation of the Kuramoto model and the synchronisation phenomenon it exhibits, we summarise recent results on the study of a generalised Kuramoto model that includes inertial effects and stochastic noise. Series: Cambridge Nonlinear Science Series. Before this, he was a Humboldt fellow at University of Wuppertal. Description: 1 online resource xix, 411 pages : illustrations, portraits. First recognized in 1665 by Christiaan Huygens, synchronization phenomena are abundant in science, nature, engineering and social life. Professor Michael Rosenblum has been a research associate in Department of Physics, Potsdam University since 1997.
The main effects are illustrated with experimental examples and figures, and the historical development is outlined. The first half of this book describes synchronization without formulae, and is based on qualitative intuitive ideas. Systems as diverse as clocks, singing crickets, cardiac pacemakers and applauding audiences exhibit a tendency to operate in synchrony. In the case of the Polar Regions heat and mass transfer through the intervening ocean and atmosphere provided the coupling. The main effects are illustrated with experimental examples and figures, and the historical development is also outlined.
Phase Locking and Frequency Entrainment: 7. Namely we apply the transform iteratively to the data. His main research interests are the application of oscillation theory and nonlinear dynamics to biological systems and time series analysis. The main effects are illustrated with experimental examples and figures, and the historical development is outlined. In the first section, we give a concise introduction to synchronizing systems, followed by a qualitative discussion in the next section of their representation in terms of interacting limit-cycle oscillators. His main research interests are nonlinear dynamics and their applications to geophysics and physiology and to time series analysis. Synchronization in the presence of noise; 10.
Discovery of synchronization by Christiaan Huygens; Appendix 2. Pikovsky: Research Arkady Pikovsky Research Topics current activities highlighted Synchronization of chaos Phase synchronization Synchronization in networks Chimera states and other patterns of synchrony Controlling synchrony Inferring synchrony and coupling properties Network reconstruction Biomedical applications Strongly nonlinear lattices: First and second sound Destruction of Anderson localization in nonlinear lattices Lyapunov exponents in disordered systems Phase compactons Compactons vs chaos in lattices Chaotic scattering Coherence resonance System-size resonance Noise in systems with delay Synchronization by common noise Common noise and coupling Lyapunov exponents and vectors Globally coupled chaotic systems Mixing flows Strange nonchaotic attractors Singular continuous spectra Renormalization group Production systems Simple systems with hyperbolic strange attractors Attractors and repellers in reversible systems Coupling sensitivity of chaos. In 2001 he will be a member of the Editorial Board of the Int. In sections three and four, we discuss how each oscillating unit, either in isolation or in interaction with other units, may be effectively described with a phase variable having a first-order dynamics in time, and then deriving the form of interaction in terms of differences of phases between the oscillators. Although more than forty years have passed since its introduction, the model continues to occupy the centre stage of research in the field of non-linear dynamics and is also widely applied to model diverse physical situations. The main effects are illustrated with experimental examples and figures, and the historical development is outlined.
The model comprises limit-cycle oscillators with distributed natural frequencies interacting through a mean-field coupling. This comprehensive text will be of interest to graduate students and specialist researchers. Using tools of statistical physics, we highlight the equilibrium and nonequilibrium aspects of the dynamics of the generalised Kuramoto model, and uncover a rather rich and complex phase diagram that it exhibits, which underlines the basic theme of intriguing emergent phenomena that are exhibited by many-body complex systems. In most other regions new methods are needed to decipher the more subtle linkages between climate and floods e. Basic notions: the self-sustained oscillator and its phase 3.