Stabilizing high-period orbits in chaos and generation of islands: a piecewise linear approach

This paper proposes a novel piecewise linear autonomous chaos generator and considers the following problems: (1) controlling chaos; and (2) generation of islands. The chaotic system is a novel version of the Manifold Piecewise Linear (MPL) system and its dynamics are governed by a piecewise linear map with hysteresis. It is noted that stabilizing high-period orbits is hard for the old MPL but is easy for the novel MPL because of the hysteresis effect in its return map. Islands are chaos whose support is the union of divided subintervals in the domain of the return map. Also, we have clarified interesting bifurcation phenomena for the islands