Chaotic behavior and chaos control for a class of complex partial differential equations

Systems of complex partial differential equations, which include the famous nonlinear Schrodinger, complex Ginzburg-Landau and Nagumo equations, as ex amples are important from a practical point of view. These equations appear in many important fields of physics. The goal of this paper is to concentr ate on this class of complex partial differential equations and study the f ixed points and their stability analytically, the chaotic behavior and chao s control of their unstable periodic solutions. The presence of chaotic beh avior in this class is verified by the existence of positive maximal Lyapun ov exponent. The problem of chaos control is treated by applying the method of Pyragas. Some conditions on the parameters of the systems are obtained analytically under which the fixed points are stable (or unstable).