Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems

Abstract

In this paper, chaos excited chaos synchronizations of generalized van der Pol systems with integral and fractional order are studied. Synchronizations of two identified autonomous generalized van der Pot chaotic systems are obtained by replacing their corresponding exciting terms by the same function of chaotic states of a third nonautonomous or autonomous generalized van der Pot system. Numerical simulations, such as phase portraits, Poincare maps and state error plots are given. It is found that chaos excited chaos synchronizations exist for the fractional order systems with the total fractional order both less than and more than the number of the states of the integer order generalized van der Pot system. (c) 2006 Elsevier Ltd. All rights reserved.