Synchronizing chaotic systems with positive conditional Lyapunov exponents by using convex combinations of the drive and response systems

Abstract We introduce a new method for synchronizing chaotic systems with positive conditional Lyapunov exponents, i.e., systems that do not synchronize in the Pecora-Carroll sense. This method works by considering a convex combination of the drive and response systems as a new driving signal. In this combination, the compoent associated with the response system acts as a chaos suppression method stabilizing the dynamics of the response system. This allows the chaotic component from the drive signal to synchronize both systems. The method is applied to synchronize some connections of the Rossler, Lorenz and van der Pol-Duffing systems that do not synchronize using the Pecora-Carroll scheme.

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