## Chaotic Synchronization: Applications to Living SystemsInteracting chaotic oscillators are of interest in many areas of physics, biology, and engineering. In the biological sciences, for instance, one of the challenging problems is to understand how a group of cells or functional units, each displaying complicated nonlinear dynamic phenomena, can interact with one another to produce a coherent response on a higher organizational level.This book is a guide to the fascinating new concept of chaotic synchronization. The topics covered range from transverse stability and riddled basins of attraction in a system of two coupled logistic maps over partial synchronization and clustering in systems of many chaotic oscillators, to noise-induced synchronization of coherence resonance oscillators. Other topics treated in the book are on–off intermittency and the role of the absorbing and mixed absorbing areas, periodic orbit threshold theory, the influence of a small parameter mismatch, and different mechanisms for chaotic phase synchronization.The biological examples include synchronization of the bursting behavior of coupled insulin-producing beta cells, chaotic phase synchronization in the pressure and flow regulation of neighboring functional units of the kidney, and homoclinic transitions to phase synchronization in microbiological reactors. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

COUPLED NONLINEAR OSCILLATORS | 1 |

TRANSVERSE STABILITY OF COUPLED MAPS | 33 |

UNFOLDING THE RIDDLING BIFURCATION | 75 |

TIMECONTINUOUS SYSTEMS | 123 |

COUPLED PANCREATIC CELLS | 177 |

CHAOTIC PHASE SYNCHRONIZATION | 211 |

### Other editions - View all

### Common terms and phrases

3-cells amplitude anti-phase asymptotic basin of attraction behavior bifurcation curve bifurcation diagram blowout bifurcation bursting cells chaos chaotic attractor chaotic dynamics chaotic oscillators chaotic phase synchronization chaotic saddle chaotic set chaotic synchronization chronization cluster coexisting coherent considered corresponding coupled logistic maps coupled oscillators coupling parameter coupling strength critical curves denotes destabilization Figure fixed point frequency globally coupled globally riddled basin Hence homoclinic Hopf bifurcation illustrated in Fig interacting interval invariant Lett limit cycle logistic maps main diagonal Maistrenko Mosekilde neighborhood nephrons noise nonlinear observed occurs one-dimensional map parameter mismatch partial synchronization period-2 cycle period-doubling bifurcation phase difference phase space phase synchronization Phys Pikovsky pitchfork bifurcation plane preimages quasiperiodic regime resonance Rossler oscillators saddle cycle saddle-node bifurcation sector shows solution stable structure subcritical supercritical synchronization manifold synchronization region synchronized chaotic torus trajectories transition transverse Lyapunov exponent transverse period-doubling transverse stability transversely unstable two-cluster two-dimensional unstable manifolds variation

### References to this book

Synchronization in Oscillatory Networks Grigory V. Osipov,Jürgen Kurths,Changsong Zhou No preview available - 2007 |

Integration of Fuzzy Logic and Chaos Theory Zhong Li,Wolfgang A. Halang,Guanrong Chen No preview available - 2006 |