Bifurcation and chaos of a particle motion system with holonomic constraint

Abstract

This paper investigates a holonomic constrained system of a particle moving on a horizontal smooth plane. The equilibrium points, bifurcations and chaotic attractors of the system are analyzed. It shows that the rich dynamic behaviors of the particle motion system, including the degenerate Hopf bifurcations at multiple equilibrium points, the chaotic behaviors of the particle motion. The numerical simulations are carried out to verify theoretical analyses and to exhibit the rich chaotic behaviors.