Computional Dynamics for Diffusionless Lorenz Equations with Periodic Parametric Perturbation

Abstract

The dynamics of diffusionless Lorenz equations (DLE) with periodic parametric perturbation is studied through numerical and experimental investigations in this paper. A method for calculating Lyapunov exponents (LEs), Lyapunov dimension (LD) from time series is presented. Furthermore, bifurcation and some complex dynamic behaviors such as periodic, quasi-periodic motion and chaos which occurred in the system are analyzed. And an algorithm for detecting unstable periodic orbits (UPOs) is presented. Also, give some numerical simulation studies of the system in order to verify the analytic results.