Dynamics Analysis of the Stochastic Lorenz System

Abstract

This paper mainly studies the dynamical behaviors of the stochastic Lorenz system, which means one parameter of Lorenz system is designed as a bounded random parameter. This stochastic system can be transformed into an equivalent deterministic nonlinear system by Chebyshev polynomial approximation, so the dynamics characteristics of the stochastic Lorenz system can be obtained by analyzing the corresponding equivalent deterministic system. Bifurcation diagram, phase graph, poincaré section are used to show that this stochastic Lorenz system shares some dynamics characteristics with the deterministic system.