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Description:The novel scheme is called F — M synchronization, since it combines the inverse generalized synchronization based on a functional relationship F with the matrix projective synchronization based on a matrix M. In particular, the proposed approach enables F — M synchronization with index d to be achieved between n-dimensional drive system map and m-dimensional response system map, where the synchronization index d corresponds to the dimension of the synchronization error. The technique, which exploits nonlinear controllers and Lyapunov stability theory, proves to be effective in achieving the F — M synchronization not only when the synchronization index d equals n or m, but even if the synchronization index d is larger than the map dimensions n and m. Finally, simulation results are reported, with the aim to illustrate the capabilities of the novel scheme proposed herein. Xt 1 Introduction The idea of synchronizing two identical chaotic systems that start from different initial conditions was introduced by Pecora and Carroll [ 1 ]. Using a transmitted signal, they showed that synchronization occurs when the Lyapunov exponents for the response subsystem are all negative.

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