The subject of chaos and, in particular, the complex chaotic patterns that can arise in distributed active systems are topics that are currently attracting much attention from various branches of science. This book and its recently published partner volume offer an excellent introduction to the basic theory of cooperative behavior in distributed active systems and are written at a level that is accessible to undergraduate students.
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This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. Such patterns can be produced autonomously by a system, or can result from selective amplification of fluctuations caused by external weak noise. Although the material in this book is often described by refined mathematical theories, we have tried to avoid a formal mathematical style. Instead of rigorous proofs, the reader will usually be offered only "demonstrations" (the term used by Prof. V. I. Arnold) to encourage intuitive understanding of a problem and to explain why a particular statement seems plausible. We also refrained from detailing concrete applications in physics or in other scientific fields, so that the book can be used by students of different disciplines. While preparing the lecture course and producing this book, we had intensive discussions with and asked the advice of Prof. V. I. Arnold, Prof. S. Grossmann, Prof. H. Haken, Prof. Yu. L. Klimontovich, Prof. R. L. Stratonovich and Prof. Ya.
This book is the second of two volumes that together give a comprehensive introduction to the theory of cooperative behavior in active systems. This volume is devoted to the properties of the complex chaotic patterns that can arise in distributed active systems. The reader will encounter strange attractors, fractals, discrete maps, spatio-temporal chaos..., and will learn how these phenomena relate to the emergence of complex and chaotic patterns. Examples treated in detail include population explosion and extinction in fluctuating distributed media, and fluctuation effects in binary annihilation.
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