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By: E Mosekilde and Y Maistrenko
Interacting 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 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 behaviour of coupled insulin-producing beta cells, chaotic phase synchronization in the pressure and flow regulation of neighbouring functional units of the kidney, and homoclinic transitions to phase synchronization in microbiological reactors. This book should be of interest to students and researchers interested in applying new concepts of chaotic synchronization and clustering to biological systems.
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