Stabilization of unstable periodic attractors of complex damped non-linear dynamical systems

In the recent paper [Int. J. Non-Linear Mech. 35 (2000) 309], periodic attractors were studied for a class of complex damped non-linear dynamical systems of the form: where z(t)=x(t)+iy(t), , the bar denotes the complex conjugate and ε is a small positive parameter. The object of this paper is to continue our investigation of this class by studying the stabilization of unstable periodic attractors of system (*). A feedback control method which is suggested by Pyragas is used to stabilize these unstable periodic attractors. We construct Poincaré plots before and after control to prove that the stabilization is achieved. Two examples are presented which served to illustrate this investigation. Maximal Lyapunov exponents and the power spectrum are calculated to show that our periodic attractors are not chaotic attractors.