Symbolic Dynamics for a Piecewise-Affine System with Hysteresis

In this paper we present the computation of symbolic dynamics of a one dimensional return map of a piecewise-affine hybrid system. The system arises as a simple electrical circuit with hysteresis switching, and exhibits chaotic dynamics. Our method allows us to rigorously obtain a qualitative description of the discrete behaviour of the system. We show how the discrete dynamics changes as a parameter is varied, and we compute bounds for the topological entropy to provide a measure of the complexity of the system.