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**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.

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.

Reviewer: Sergiy Yanchuk (Kyïv)

### MSC:

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 |