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Chaotification of Fractional Maps

C. LI, L. MA, H. XIAO

Abstract


Fractional difference equations, or fractional maps, appear at least in two ways. One way is that some of them directly come from the discrete dynamical process with memory or heredity. Another one is that some of them are originated from the discretization of the continuous fractional differential equations. Such maps may be not chaotic. On the other hand, anti-control of chaos (or chaotification for brevity) has potential applications in secure communication. In this paper, we make non-chaotic fractional maps chaotic by constructing suitable controllers. The presented control technique and method has been applied to the non-chaotic fractional Hénon map, which become chaotic via the designed controllers. The computer graphics are also displayed to show the efficiency of the designed controllers

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