Strange attractors and chaos control in periodically forced complex Duffing's oscillators

An interesting and challenging research subject in the field of nonlinear dynamics is the study of chaotic behavior in systems of more than two degrees of freedom. In this work we study fixed points, strange attractors, chaotic behavior and the problem of chaos control for complex Duffing's oscillators which represent periodically forced systems of two degrees of freedom. We produce plots of Poincaré map and study the fixed points and strange attractors of our oscillators. The presence of chaotic behavior in these models is verified by the existence of positive maximal Lyapunov exponent. We also calculate the power spectrum and consider its implications regarding the properties of the dynamics. The problem of controlling chaos for these oscillators is studied using a method introduced by Pyragas (Phys. Lett. A 170 (1992) 421), which is based on the construction of a special form of a time-continuous perturbation. The study of coupled periodically forced oscillators is of interest to several fields of physics, mechanics and engineering. The connection of our oscillators to the nonlinear Schrödinger equation is discussed.