碰撞振动系统中周期轨擦边诱导的混沌激变

基于图胞映射理论, 提出了一种擦边流形的数值逼近方法, 研究了典型Du ng 碰撞振动系统中擦边诱导激变的全局动力学. 研究表明, 周期轨的擦边导致的奇异性使得系统同时产生1 个周期鞍和1 个混沌鞍. 当该周期鞍的稳定流形与不稳定流形发生相切时, 边界激变发生使得该混沌鞍演化为混沌吸引子. 噪声可以诱导周期吸引子发生擦边, 这种擦边导致了1 种内部激变的发生, 表现为该周期吸引子与其吸引盆内部的混沌鞍发生碰撞后演变为1 个混沌吸引子.

GRAZING-INDUCED CHAOSTIC CRISIS FOR PERIODIC ORBITS IN VIBRO-IMPACT SYSTEMS

A numerical approximation of grazing manifold is proposed via the digraph cell mapping method. The global dynamics of grazing-induced crisis for a typical Du ng vibro-impact system are then investigated. The results reveal that, the singularity caused by the grazing nature of periodic orbits can induce a bifurcation where a periodic saddle and a chaotic saddle arise simultaneously. When the stable and unstable manifolds of the periodic saddle undergo the tangency, a boundary crisis occurs and a chaotic attractor is then brought from the chaotic saddle. Also, grazing phenomenon of periodic orbits induced by noise can be observed. This grazing phenomenon can induce a novel interior crisis, where a chaotic attractor arises due to the collision of this periodic attractor and the chaotic saddle.