Anti-synchronization on autonomous and non-autonomous chaotic systems via adaptive feedback control

In this paper, the anti-synchronization of a general class of chaotic systems is investigated. A simple adaptive feedback scheme is proposed to anti-synchronize many familiar chaotic systems, including autonomous systems and non-autonomous systems. Lyapunov analysis for the error system gives the asymptotic stability conditions based on the invariance principle of differential equations. The schemes are successfully applied to three groups of examples: the van der Pol-Duffing oscillator, the parametrically harmonically excited 4D system, and the additionally harmonically excited Murali-Lakshmanan-Chua circuit. Numerical results are presented to justify the theoretical analysis in this paper.