BOUNDARY SURFACES AND BASIN BIFURCATIONS IN CHUA'S CIRCUIT

Abstract

One of the most important tasks in the analysis of a nonlinear system is to determine its global behavior and, in particular, to delineate the domains of attraction for asymptotically stable solutions. Stable manifolds often act as boundary surfaces between such domains in the state space. In this paper the morphology of boundary surfaces is studied in a single member of Chua's circuit family, although the techniques used apply equally well to many other nonlinear circuits. Of all the PWL circuits known so far which exhibit two stable states it is typical that their resistor characteristics each have at least three segments. Although bistability cannot be achieved via a 2-segment characteristic in the plane, complicated bistable behavior, including chaotic attractors, can occur locally at the boundary of two linear regions in the 3-D Chua's circuit, i.e. bistability is achieved with a minimal number of segments. By using a 3-segment characteristic, at least five attractors can be generated. Basin structure of the corresponding attractors is examined using numerical simulations. Period-adding, symmetry-breaking and remerging bifurcation phenomena are observed experimentally and numerically from an extended Chua's circuit. Dynamical properties of sequential circuits can be investigated by means of switching between the system's attractors, and boundary surfaces play a crucial role in the process of switching. The use of basin delineation in the triggering of multistable circuits is shown.