On the Stability and Bifurcation Phenomena Associated with Dynamical Systems

Abstract

These lectures are concerned with the bifurcation and stability behaviour of general dynamical systems. Emphasis is on multiple-parameter autonomous systems, and both static and dynamic bifurcations associated with such systems are explored analytically. Thus, Hopf and degenerate Hopf bifurcations, as well as bifurcations into quasi-periodic motions on invariant tori are analysed. A brief discussion concerning the analysis of non-autonomous systems is presented in the last chapter.