and Prerequisites.- Basic Nonlinear Phenomena.- Applications and Extensions.- Principles of Continuation.- Calculation of the Branching Behavior of Nonlinear Equations.- Calculating Branching Behavior of Boundary-Value Problems.- Stability of Periodic Solutions.- Qualitative Instruments.- Chaos.
Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.
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.