Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos

This book contains computational methods for numerically computing steady state and Hopf bifurcations. It is probably the first textbook to describe these types of numerical bifurcation techniques. The book requires only a basic knowledge of calculus, and uses detailed examples, problems, and figures. This will be appropriate as a textbook for graduate students.

This book covers the central role that bifurcations play in nonlinear phenomena, explaining mechanisms of how stability is gained or lost. It emphasizes practical and computational methods for analyzing dynamical systems. A wide range of phenomena between equilibrium and chaos is explained and illustrated by examples from science and engineering. The book is a practical guide for performing parameter studies and includes exercises.

Combining an introduction on the textbook level with an exposition of computational methods, this book addresses the mathematical needs of scientists and engineers. It should be of interest to those in a wide variety of disciplines, including physics, mechanical engineering, electrical engineering, chemistry and chemical engineering, biology, and medicine. Both graduate students (in courses on dynamical systems, stability analysis, differential equations, and chaos) and professionals will be able to use the book equally well. The introduction avoids mathematical formalism, and the only required background is calculus.

In the third edition there is a chapter on applications and extensions of standard ODE approaches, for example, to delay equations, to differential-algebraic equations, and to reaction-diffusion problems. Additional material is inserted, including the topics deterministic risk, pattern formation, and control of chaos, and many further references.

Review of Earlier Edition:

"The outcome is impressive. The book is beautifully written in a style that seeks not only to develop the subject matter but also to expose the thought processes behind the mathematics." Proceedings of the Edinburgh Mathematical Society