Abstract
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.
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