Hopf bifurcation in a control system for the Washout filter-based delayed neural equation

Washout filter is a simple filter that can be designed easily. In this paper, a system for controlling a neural equation with discrete time delay based on Washout filter is presented. The transcendental equation of the corresponding linearized system is analyzed. In this control system, it is found that Hopf bifurcation occurs when the control parameters are chosen properly and that a chaotic orbit can be controlled to a stable periodic solution. The stability condition for bifurcating periodic solutions and the direction of Hopf bifurcation are studied by applying the normal form theory and the center manifold theorem. Some numerical results are also presented to illustrate the correctness of our results.