Chaos control of chaotic limit cycles of real and complex van der Pol oscillators

Chaos control and nonlinear dynamics of both real and complex nonlinear oscillators constitutes some of the most fascinating developments in applied sciences. The chaos control of chaotic unstable limit cycles of real and complex (or coupled) nonlinear van der Pol oscillators is investigated in this paper. These oscillators appear in many important applications in engineering, for example, vacuum tube circuits. The presence of chaotic limit cycles is verified by calculating largest Lyapunov exponent and the power spectrum. The problem of chaos control of these limit cycles is studied using a feedback control method, which is based on the construction of a special form of a time-continuous perturbation. Our investigation of both real and complex (or coupled) van der Pol oscillators enriches the nonlinear dynamical systems. (C) 2003 Elsevier Ltd. All rights reserved.