振动筛系统的两类余维三分岔与非常规混沌演化

建立了振动筛系统的动力学模型，推导出了其周期运动的Poincaré 映射，基于Poincaré 映射方法着重研究了系统Flip-Hopf-Hopf余维三分岔、三次强共振条件下的Hopf-Hopf余维三分岔以及三种非常规的混沌演化过程.研究结果表明，此两类余维三分岔点附近的动力学行为变得更加复杂和新颖，在分岔点附近出现了三角形吸引子、3T²环面分岔以及“五角星型”、“轮胎型”概周期吸引子，揭示了环面爆破、环面倍化以及T²环面分岔向混沌演化的过程，这些结果对于振动筛系统的动力学优化设计提供了理论参考.关键词：余维三分岔非常规混沌演化T²环面分岔')" href="#">T²环面分岔

Two codimension-3 bifurcations and non-typical routes to chaos of a shaker system

The dynamical model and Poincaré maps of a shaker are established. Two types of codimension-3 bifurcations of this system, including Flip-Hopf-Hopf bifurcation and Hopf-Hopf bifurcation in the third order strong resonant case, and three non-typical routes to chaos are investigated by using Poincaré maps. The system exhibits more complicated dynamic behaviors near the points of codimension-3 bifurcation. The results show that near the points of bifurcation there existtriangle attractor, 3T² torus bifurcation and “pentalpha-like”, “tire-like” attractors in projected Poincaré sections. The routes to chaos via torus explosion, torus-doubling bifurcation and T² torus bifurcation are analyzed by numerical simulation. The system parameters of shaker may be optimized by studying the stability and bifurcation of periodic motion of the shaker.