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 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.

Contents:

• Coupled Nonlinear Oscillators
• Transverse Stability of Coupled Maps
• Unfolding the Riddling Bifurcation
• Time-Continuous Systems
• Coupled Pancreatic Cells
• Chaotic Phase Synchronization
• Population Dynamic Systems
• Clustering of Globally Maps
• Interacting Nephrons
• Coherence Resonance Oscillators