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

An interesting and challenging research subject in the field of nonlinear d ynamics is the study of chaotic behavior in systems of more than two degree s of freedom. In this work we study fixed points, strange attractors, chaot ic behavior and the problem of chaos control for complex Duffing's oscillat ors which represent periodically forced systems of two degrees of freedom. We produce plots of Poincare map and study the fixed points and strange att ractors of our oscillators. The presence of chaotic behavior in these model s is verified by the existence of positive maximal Lyapunov exponent. We al so calculate the power spectrum and consider its implications regarding the properties of the dynamics. The problem of controlling chaos for these osc illators 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 tim e-continuous perturbation. The study of coupled periodically forced oscilla tors is of interest to several fields of physics, mechanics and engineering . The connection of our oscillators to the nonlinear Schrodinger equation i s discussed. (C) 2001 Elsevier Science B.V. All rights reserved.