A search algorithm of bifurcation point in an impact oscillator with periodic threshold

In this paper, we propose a search algorithm of bifurcation point in an impact oscillator with periodic threshold. The algorithm based on the Poincaré map approach. In particular, we target the periodic threshold as the bifurcation analysis parameter. First, we define the composite Poincaré map of the two-dimensional impact oscillator. Next, we show the derivative of the Poincaré map with a parameter of the threshold. Finally, we apply the algorithm for a rigid overhead wire-pantograph system. The validity of the algorithm will be verified by the analyses results.