Synchronization: a universal concept in nonlinear sciences. (English) Zbl 0993.37002

Cambridge Nonlinear Science Series. 12. Cambridge: Cambridge University Press. xx, 411 p. (2001).
The book deals with different kinds of synchronization phenomena. Starting with the very basic introduction, the authors explain the notion of synchronization in detail. Different types of synchronization are considered including phase and complete synchronization. First, the authors review the classical theory of synchronization of periodic oscillators. Then, recent results on the synchronization of chaotic systems, systems with noise are presented. The considered models are forced oscillators, ensembles of coupled oscillators as well as spatially distributed systems. Many examples of real systems and mathematical models are provided with the emphasis on interdisciplinary applications.
The book is addressed to a broad readership: experimentalists as well as theoreticians. Part I, “Synchronization without formulae”, describes the main notions on the qualitative level with many examples. The same ideas are presented in Parts II and III but on the quantitative level with the use of nonlinear dynamics tools. An extensive bibliography is also provided.


37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37C75 Stability theory for smooth dynamical systems
37C80 Symmetries, equivariant dynamical systems (MSC2010)
34C23 Bifurcation theory for ordinary differential equations
34C30 Manifolds of solutions of ODE (MSC2000)
92B05 General biology and biomathematics
93C15 Control/observation systems governed by ordinary differential equations
34F05 Ordinary differential equations and systems with randomness