Rigorous Analysis of Chua’s Circuit With a Smooth Nonlinearity

Abstract

Dynamics of Chua’s circuit with a smooth nonlinearity is studied by means of interval arithmetic methods. We analyze behaviors of the system for several parameter values in the periodic and chaotic regions. For parameter values in the chaotic region, we find lower bounds for the topological entropy of a corresponding return map and prove that the system is chaotic in the topological sense. We find low-period orbits embedded in chaotic attractors and estimate the true value of the topological entropy. We construct a trapping region enclosing the spiral attractor and discuss how to prove the existence of a trapping region for the case of the double-scroll attractor.