Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need.

Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in the book have been developed only recently and have not yet appeared in textbook form.

In keeping with the self-contained nature of the book, all the topics are developed with introductory background and complete mathematical rigor. Generously illustrated and written at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.

Contents:

• Structurally Stable Systems
• Bifurcations of Dynamical Systems
• The Behavior of Dynamical Systems on Stability Boundaries of Equilibrium States
• The Behavior of Dynamical Systems on Stability Boundaries of Periodic Trajectories
• Local Bifurcations on the Route Over Stability Boundaries
• Global Bifurcations at the Disappearance of a Saddle-Node Equilibrium States and Periodic Orbits
• Bifurcations of Homoclinic Loops of Saddle Equilibrium States
• Safe and Dangerous Boundaries

"The book is a welcome addition to the literature on bifurcation theory. In particular, Chapters 12 and 13 contain a wealth of material on global bifurcations (particularily on those of codimension two) that has not been published in a textbook before. The book is well-written and nicely illustrated, while being mathematically rigorous (in places quite technical). It will be of interest to anyone, including dedicated non-specialist readers, from about graduate level onwards, who want to learn about the mathematical theory of (global) bifurcations."

“The book is a welcome addition to the classical list of books on bifurcation theory. It is an advanced book, attempting to be more general in the abstract theory of this theory. It is very well written and contains a large number of explanatory footnotes and pictures. As such, it is very instructive even for researchers well initiated in the subject. It is also suitable as a textbook, albeit at an advanced level. Thus, it is a 'must' for everyone seriously interested in bifurcation theory.”