Open AccessTwo codimension-3 bifurcations and non-typical routes to chaos of a shaker system
Author(s) -
Yongxiang Zhang,
Guiqin Kong,
Jing Yu
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.6182
Subject(s) - shaker , saddle node bifurcation , transcritical bifurcation , torus , bogdanov–takens bifurcation , pitchfork bifurcation , biological applications of bifurcation theory , attractor , hopf bifurcation , homoclinic bifurcation , bifurcation , codimension , bifurcation diagram , period doubling bifurcation , mathematics , infinite period bifurcation , mathematical analysis , physics , nonlinear system , geometry , quantum mechanics , vibration
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.