Bifurcation theory and methods of dynamical systems. (English) Zbl 0961.37015

Luo, Dingjun; Wang, Xian; Zhu, Deming; Han, Maoan

World Scientific Advanced Series in Dynamical Systems. 15. Singapore: World Scientific. xiii, 461 p. (1997).

This monograph is devoted to the theory of bifurcation and dynamical systems defined by ordinary differential equations. Chapter 1 contains a review of some basic concepts and general results. Chapter 2 deals with several kinds of limit cycle bifurcation of two dimensional systems. In chapter 3 some applied models together with the planar Liénard system are presented. In chapter 4 the authors consider higher order systems. A discussion of the bifurcation of local periodic solutions, and the method of Liapunov-Schmidt, averaging and integral manifolds are developed. Chapter 5 is concerned with the Hopf bifurcation. Some chaotic dynamics are also considered. The last chapter is concerned with the persistence and transversality of homoclinic and heteroclinic loops. The monograph is very well written and contains a lot of information on bifurcation and dynamical systems. Many examples are treated. The clear presentation makes the reading quite easy.
This is a nice addition to the literature on bifurcation and dynamical systems.

Reviewer: Abdelkader Boucherif (Dhahran)

MSC:

37G15	Bifurcations of limit cycles and periodic orbits in dynamical systems
37-02	Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory

Keywords:

bifurcation theory; dynamical systems; structural stability; unfoldings; homoclinic and heteroclinic orbits; integral manifolds; Liapunov-Schmidt reduction; Melnikov vector