Torus doubling and hyperchaos in a five dimensional hysteresis circuit

Abstract

This article discusses a simple five dimensional autonomous circuit that includes one piecewise linear hysteresis element. We derive theoretical formulae of its three dimensional return map, its Jacobian matrix and Jacobian. Applying these to evaluate Lyapunov exponents, we clarify torus doubling route to area expanding chaos and volume expanding chaos which is a kind of hyperchaos. We also investigate basic bifurcation of these phenomena. Some attractors from the return map are verified by laboratory measurements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>