On Bifurcations Leading to Chaos in Chua's Circuit

Abstract

Bifurcations and the structure of limit sets are studied for a three-dimensional Chua's circuit system with a cubic nonlinearity. On the base of both computer simulations and theoretical results a model map is proposed which allows one to follow the evolution in the phase space from a simple (Morse-Smale) structure to chaos. It is established that the appearance of a complex, multistructural set of double-scroll type is stimulated by the presence of a heteroclinic orbit of intersection of the unstable manifold of a saddle periodic orbit and unstable manifold of an equilibrium state of saddle-focus type.