Abstract
Recently, numerous chaotic systems in the form of fractional difference equations have received considerable attention. Based on the stability theory of linear fractional difference systems, this chapter presents combined synchronization between fractional-order chaotic maps described by the left Caputo difference operator. Some nonlinear controllers are designed, which enable synchronization to be achieved between different fractional-order chaotic maps with different dimensions. The 2D fractional Lozi, Lorenz, and Flow maps, as well as the 3D fractional Wang, Rössler, and Stefanski maps, have been taken to show the combined synchronization. The results of these synchronization laws are experimentally investigated to ensure that the synchronization errors converge to zero.
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