Takuji Kousaka, Tetsushi Ueta, YUE MA, Hiroshi Kawakami, Bifurcation analysis of a piecewise smooth system with non-linear characteristics, World Scientific, International Journal of Circuit Theory and Applications, Vol.33, No.4, pp.263-279, July 2005.
Abstract: In previous works, there are no results about the bifurcation analysis for a piecewise smooth system with non-linear characteristics. The main purpose of this study is to calculate the bifurcation sets for a piecewise smooth system with non-linear characteristics. We first propose a new method to track the bifurcation sets in the system. This method derives the composite discrete mapping, Poincare mapping. As a result, it is possible to obtain the local bifurcation values in the parameter plane. As an illustrated example, we then apply this general methodology to the Rayleigh-type oscillator containing a stateperiod- dependent switch. In the circuit, we can find many subharmonic bifurcation sets including global bifurcations. We also show the bifurcation sets for the border-collision bifurcations. Some theoretical results are verified by laboratory experiments.