Takuji Kousaka, Ken'ichi Fujimoto, YUE MA, Tetsushi Ueta, Hiroshi Kawakami, Bifurcations observed in BVP oscillator with periodically switched RC circuit, Watam Press, Dynamics of Continuous, Discrete and Impulsive Systems. Series A: Mathematical Analysis, Vol.16, No.6, 811-824, Waterloo, Nov. 2009.
Abstract: Many works have been devoted to the study of the behavior of the Bonhoe er-van der Pol (BVP) oscillator in physiological and biochemical modeling studies. In this paper, bifurcation and chaos in BVP oscillator, which is intermittently connected to a parallel RC load, is investigated. By using the periodicity of switching action we introduce a composite discrete mapping as the Poincar´e mapping that is useful for the analysis of piecewise nonlinear systems. Adjusting the switching period close to the integral multiple of the period of self-oscillation, we find various synchronizations. In particular the fundamental synchronization is discussed. Under the appropriate switching ratios, we illustrate that the synchronized state bifurcates to chaotic states by the period doubling cascades or the torus breaking down.