バウンシングボール系に生じるカオス転移メカニズム

抄録

In this study, we focus on the bouncing ball system with a periodically oscillating boundary. In the system, it is known that chaotic behavior arises. The bouncing ball system have application in various engineering systems. We have studied the system and found that the maximum value of ball height is changed stepwisely varying increase of the periodically oscillating boundary’s frequency. The purpose of this study is to clarify the mechanism arising the stepwise bifurcation. In this paper, we measure the displacements of the ball before and after the bifurcation point, and investigate the change of dynamics by Poincaré maps. Moreover, it's clear that the number of cycles of the boundary during a single bouncing is close to an integer value just before the height of the ball is maximized when stepwise bifurcation is occurred.