Dynamic analysis for the hyperchaotic system with nonholonomic constraints

This paper first formulates a new hyperchaotic system for particle motion and analyzes the equilibrium stability of the system and the hyperchaotic behaviors in the motion of the particle on a horizontal smooth plane. We then investigate the influences of two nonlinear nonholonomic constraints on the particle motion. The numerical simulations, including bifurcation diagrams, computation of Lyapunov exponents, Poincaré maps, and phase portraits for systems, not only show the hyperchaotic phenomena, but also exhibit the different hyperchaotic behaviors in the constrained parameters space for the various regimes. Additionally, a holonomic constraint is introduced to control the hyperchaotic system.