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

Abstract

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.