Dynamics Analysis of the Stochastic Lorenz System

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 intoan equivalent deterministic nonlinear system by Chebyshevpolynomial approximation, so the dynamics characteristics ofthe stochastic Lorenz system can be obtained by analyzingthe corresponding equivalent deterministic system. Bifurcationdiagram, phase graph, poincarée section are used to showthat this stochastic Lorenz system shares some dynamicscharacteristics with the deterministic system.