Bifurcation analysis in hybrid nonlinear dynamical systems

In this paper, we investigate the bifurcation phenomena in the nonlinear dynamical system switched by a threshold of the state or a periodic interrupt. First, we propose a method to trace the bifurcation sets for above system. We derive the composite discrete mapping as Poincare mapping. As a result, it is possible to obtain the local bifurcation values in the parameter plane. We also propose an efficient analyzing method for border-collision bifurcations. As an illustrated example, we investigate the behavior of the Rayleigh-type oscillator switched by a threshold of the state or a periodic interrupt. In this system, we can find many subharmonic bifurcation sets including global bifurcations and border collision. Some theoretical results are verified by laboratory experiments.