Anti-control of Hopf bifurcation in derivative Lorenz chaotic system based on washout-filter

Abstract

In this paper, a derivative Lorenz chaotic system is considered and the stability of equilibrium points and the existence of Hopf bifurcation are investigated by center manifold theorem and normal form theory. Besides, we designed a washout controller such that the derivative Lorenz chaotic system undergoes a controllable Hopf bifurcation. By the calculation of the first Lyapunov coefficient and adjust the controller parameters, we can control the Hopf bifurcation phenomenon of the equilibrium. Finally, numerical simulation is given to illustrate the theoretical analysis.