## Synchronization: A Universal Concept in Nonlinear SciencesFirst recognized in 1665 by Christiaan Huygens, synchronization phenomena are abundant in science, nature, engineering and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. The first half of this book describes synchronization without formulae, and is based on qualitative intuitive ideas. The main effects are illustrated with experimental examples and figures, and the historical development is outlined. The remainder of the book presents the main effects of synchronization in a rigorous and systematic manner, describing classical results on synchronization of periodic oscillators, and recent developments in chaotic systems, large ensembles, and oscillatory media. This comprehensive book will be of interest to a broad audience, from graduate students to specialist researchers in physics, applied mathematics, engineering and natural sciences. |

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### Contents

Chapter 1 Introduction | 1 |

Part I Synchronization without formulae | 25 |

Part II Phase locking and frequency entrainment | 173 |

Part III Synchronization of chaotic systems | 299 |

Appendices | 355 |

371 | |

405 | |

### Other editions - View all

Synchronization: A Universal Concept in Nonlinear Sciences Arkady Pikovsky,Michael Rosenblum,Jürgen Kurths No preview available - 2001 |

### Common terms and phrases

amplitude analysis appears assume attractor average bifurcation called cells changes chaos chaotic Chapter circle clocks close complete consider constant corresponds coupling curve depends described determined detuning diffusion direction discuss distribution driven dynamics effect entrainment equation et al example exists experiments external force Figure firing fixed fluctuations frequency function identical illustrate important increase initial interaction interval introduce limit cycle linear locking Lyapunov exponent mean mean field measure mechanism modulation motion natural noise noisy nonlinear Note observed obtain occurs orbits original oscillators parameters particular pendulum periodic perturbation phase phase difference physical plot position possible potential present properties pulse regime relation rhythm rotation self-sustained oscillators shift shown signal solution space stable strong studied synchronization synchronization region theory threshold trajectories transition transverse unstable variable varied weak zero