Hopf Bifurcation for λ²=1 and Chaos of a Two-Degree-of-Freedom Manipulator
Zheng Xiaowu
(Department of Applied Mechanics and Engineering Southwest Jiaotong University, 610031, Chengdu, China)

Abstract: The Hopf bifurcation and chaos of a mechanical system with periodic coefficients are investigated while its periodic motion is losing stability. The differential motion equations are given with Lagrange equations, and the perturbed differential equations with periodic coefficients are derived.  The Poincar  map of the period motion is established following the Floquet theory . Furthermore, the probability of the subharmonic bifurcation, Hopf bifurcation and periodic-doubling bifurcation generation is analyzed according to the eigen-matrix with a pair of Eigenvalues crossing the unit circle from -1. The  numerical simulation results reveal that while the parameter changes, the periodic motion may result in  period 2 motion via subharmonic bifurcation, or quasi periodic motion via Hopf bifurcation, which leads to chaos motion via subharmonic bifurcation and periodic-doubling bifurcation.
Keywords: period coefficients, mechanical system, period motion, poincar  map, hopf bifurcation, chaos.