Stabilizing DLEs system with periodic parametric perturbations using backstepping control

The dynamics of diffusionless Lorenz equations (DLEs) with periodic parametric perturbation is studied through numerical simulations in this paper. Furthermore, bifurcation and some complex dynamic behaviors such as periodic, quasi-periodic motion and chaos are analyzed. Also Lyapunov exponents (LEs), Lyapunov dimension (LD) are calculated and phase portraits, Poincare sections, bifurcation diagrams are observed. Finally an backstepping controller for DLEs with periodic parametric perturbation with one unknown parameter is designed. And numerical simulations are carried out in order to verify the analytic results.