Arkady Pikovsky was part of the Max-Planck research group on nonlinear dynamics, before becoming a professor at the University of Potsdam, Germany. A member of the German and American Physical Societies, he is also part of the Editorial Board of Physical Reviews E for the term 2000-2002. Before this, he was a Humboldt fellow at University of Wuppertal. His PhD focusses on the theory of chaos and nonlinear dynamics, and was carried out at the Institute of Applied Physics of the USSR Academy of Sciences. 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.
Preface
1. Introduction
Part I. Synchronization Without Formulae: 2. Basic notions: the self-sustained oscillator and its phase
3. Synchronization of a periodic oscillator by external force
4. Synchronization of two and many oscillators
5. Synchronization of chaotic systems
6. Detecting synchronization in experiments
Part II. Phase Locking and Frequency Entrainment: 7. Synchronization of periodic oscillators by periodic external action
8. Mutual synchronization of two interacting periodic oscillators
9. Synchronization in the presence of noise
10. Phase synchronization of chaotic systems
11. Synchronization in oscillatory media
12. Populations of globally coupled oscillators
Part III. Synchronization of Chaotic Systems: 13. Complete synchronization I: basic concepts
14. Complete synchronization II: generalizations and complex systems
15. Synchronization of complex dynamics by external forces
Appendix 1. Discovery of synchronization by Christiaan Huygens
Appendix 2. Instantaneous phase and frequency of a signal
References
Index.
Cycling attractors of coupled cell systems and dynamics with symmetry.- Modelling diversity by chaos and classification by synchronization.- Basic Principles of Direct Chaotic Communications.- Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems.- Generalization of the Feigenbaum-Kadanoff-Shenker Renormalization and Critical Phenomena Associated with the Golden Mean Quasiperiodicity.- Synchronization and clustering in ensembles of coupled chaotic oscillators.- Nonlinear Phenomena in Nephron-Nephron Interaction.- Synchrony in Globally Coupled Chaotic, Periodic, and Mixed Ensembles of Dynamical Units.- Phase synchronization of regular and chaotic self-sustained oscillators.- Control of dynamical systems via time-delayed feedback and unstable controller.
