Simulation and analysis of Lorenz system's dynamics characteristics

Abstract

Chaos is similar to stochastic process in deterministic system. A nonlinear dynamics system may exhibit chaotic phenomenon if its parameters match certain combinations. This paper studied the Lorenz system through numeric simulation using phase graph and power spectrum method. It examined the nonlinear properties of the Lorenz system by varying the state parameters in both time and frequency field. It is found that 1) the chaotic patterns of the Lorenz system might emerge out of Pomeau-Manneville route and its intermittence was related to Hopf bifurcation and period-doubling bifurcation; 2) the system had to go through a series of period-doubling bifurcation routes before reaching chaotic state.