An Analytical Prediction of Periodic Flows in the Chua Circuit System

In this paper, periodic and chaotic behaviors in the Chua circuit system are investigated, and the analytical prediction of periodic flows in such a system is carried out. The solutions of the system in different regions with different parameters are first obtained. The switching boundaries are introduced for systems switching because of different system parameters in different domains. In the vicinity of the switching boundaries, the normal vector-field product is introduced to measure flow switching on the separation boundary, and the conditions for grazing and passable flows to the discontinuous boundary are presented. The basic mappings are defined and periodic responses of such a system are predicted analytically from mapping structures. The local stability and bifurcation analysis are carried out.