<p>In this paper, periodic motions in a periodically impulsive, damped pendulum system are obtained through a semi-analytical method with impulsive laws, and the saddle-node and period-doubling bifurcations are obtained, and the impulsive homoclinic orbits are also achieved. The homoclinic bifurcation does not imply that chaos exists, but it indeed implies the different types of periodic motions switch. For instance, unstable impulsive periodic motions through such homoclinic bifurcations are from librational to rotational, vice versa. The impulsive periodic motions and impulsive homoclinic orbits of the impulsive forced pendulum are also illustrated for a better understanding of impulsive periodic motions in the impulsively forced pendulum. Through this study, infinite impulsive homoclinic orbits related to all impulsive periodic motions can be found.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

On periodic motions and homoclinic bifurcations in a periodically impulsive, damped pendulum

  • Albert C. J. Luo,
  • Tianji Ma

摘要

In this paper, periodic motions in a periodically impulsive, damped pendulum system are obtained through a semi-analytical method with impulsive laws, and the saddle-node and period-doubling bifurcations are obtained, and the impulsive homoclinic orbits are also achieved. The homoclinic bifurcation does not imply that chaos exists, but it indeed implies the different types of periodic motions switch. For instance, unstable impulsive periodic motions through such homoclinic bifurcations are from librational to rotational, vice versa. The impulsive periodic motions and impulsive homoclinic orbits of the impulsive forced pendulum are also illustrated for a better understanding of impulsive periodic motions in the impulsively forced pendulum. Through this study, infinite impulsive homoclinic orbits related to all impulsive periodic motions can be found.