Numerical method for bifurcation analysis in an impact oscillator with fixed border

Impact oscillators appear in various fields such as nervous system, ecological system, and mechanical system. These systems have a characteristic property that the dynamics discontinuously behaves due to jumps at hitting borders in the state space. In general, it is difficult to obtain analytical solutions in this class. Thus a numerical method is indispensable for the bifurcation analysis in the impact oscillators; however, unfortunately, it has not been established. Therefore, we proposed a numerical method for the bifurcation analyses in the impact oscillator with a fixed border and applied the proposed method to the Rayleigh-type oscillator.