振动筛系统的两类余维三分岔与非常规混沌演化

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

建立了振动筛系统的动力学模型,推导出了其周期运动的Poincarē映射,基于Poincarē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.

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 nontypical 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 exist triangle attractor, 3 T^2 toms bifurcation and ＂pentalpha-like＂, ＂tire-like＂ attractors in projected Poincaré sections. The routes to chaos via toms explosion, toms-doubling bifurcation and T^2 toms 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.