Anti-control of Hopf bifurcation for Chen's system through washout filters

In this paper, we consider the problem of anti-controlling bifurcations for Chen's system, that is, a certain bifurcation is created at a desired location with preferred properties by appropriate control. Washout-filter-aided dynamic feedback control laws are developed for the creation of Hopf bifurcations. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. Conditions are given to determine the directions and stabilities of the bifurcating periodic solutions. We also find that this control laws can be applied to Chen's system for the purpose of control and anti-control of chaotic attractor. Finally, some numerical simulations are given to illustrate the effectiveness of the results found.