Studies of nonlinear phenomena which occur in mathematical models and which are observed in experiments profit both from a general knowledge of the theory of dynamical systems and bifurcations, and from the experience accumulated in an interpretation of specific examples. The most interesting and important nonlinear phenomenon that has come to prominence recently is the chaotic behaviour of deterministic dissipative systems. The investigation of chaotic dynamics has undergone an explosive development over the past ten years but the results are still mostly scattered throughout the journal literature.

The number of interested students and research workers from diverse fields, ranging from mathematics and physics to engineering sciences and biology, increases continuously and many of them will find it useful to have an introductory text, that surveys both theoretical and experimental aspects of chaotic behaviour. We have attempted to provide this in the present book.

The introductory chapter discusses the significance of chaos as a model of many seemingly random processes in nature and a definition of the class of dissipative systems that we will study.

The second chapter considers basic notions of the theory of dynamical systems. The difference between linear and nonlinear systems is illustrated and asymptotic behaviour is discussed in more detail. Definitions of chaos and of strange attractors and a description of chaotic behaviour in the frame of ergodic theory are then surveyed.

The third chapter deals with qualitative changes of asymptotic behaviour as a chosen parameter is varied. These changes (‘bifurcations’) may lead to chaos in several well-defined routes. The role of bifurcation theory in understanding the onset of chaos is illustrated by a number of characteristic examples.