TWO-PARAMETER STUDY OF TRANSITION TO CHAOS IN CHUA'S CIRCUIT: RENORMALIZATION GROUP, UNIVERSALITY AND SCALING

Abstract

A complex fine structure in the topography of regions of different dynamical behavior near the onset of chaos is investigated in a parameter plane of the 1D Chua's map, which describes approximately the dynamics of Chua's circuit. Besides piecewise-smooth Feigenbaum critical lines, the boundary of chaos contains an infinite set of codimension-2 critical points, which may be coded by itineraries on a binary tree. Renormalization group analysis is applied which is a generalization of Feigenbaum's theory for codimension-2 critical points. Multicolor high-resolution maps of the parameter plane show that in regions near critical points having periodic codes, the infinitely intricate topography of the parameter plane reveals a property of self-similarity.