On fundamental bifurcations from a hysteresis hyperchaos generator

In this paper we discuss a four-dimensional autonomous circuit which includes one hysteresis element. This circuit is governed by two symmetric three dimensional linear equations which are connected to each other by hysteresis switchings. Then we can derive the two-dimensional return map and show the following novel results: 1) Fundamental bifurcation diagram from periodic attractor to hyperchaos. It includes coexistence of torus and periodic attractor; 2) two-parameters bifurcation diagram. It exhibits some regularities for the onset of some periodic attractors and tori; 3) laboratory measurements of the return map attractors; 4) a sufficient condition for the existence of attractors