GLOBAL ANALYSIS AND CHAOTIC DYNAMICS OF SIX-DIMENSIONAL NONLINEAR SYSTEM FOR AN AXIALLY MOVING VISCOELASTIC BELT

Abstract

An analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of an axially moving viscoelastic belt is given in this paper for the first time. We combine the theory of normal form and the global perturbation method to investigate the global bifurcations and chaotic dynamics of the axially moving viscoelastic belt. Firstly, the theory of normal form is used to reduce six-dimensional averaged equation to the simpler normal form. Then, the global perturbation method is employed to analyze the global bifurcations and chaotic dynamics of six-dimensional nonlinear system. The analysis results indicate that there exist the homoclinic bifurcations and the single-pulse in six-dimensional averaged equation. Finally, numerical simulations are also used to investigate the nonlinear dynamic characteristics of the axially moving viscoelastic belt. The results of numerical simulations demonstrate that there exist the chaotic motions and the jumping orbits of the axially moving viscoelastic belt.