Chaotic synchronization between linearly coupled discrete fractional Hénon maps

Chaotic synchronization between linearly coupled discrete fractional Hénon maps is investigated in this paper. We obtain the numerical formula of discrete fractional Hénon map by utilizing the discrete fractional calculus. We tune the linear coupling parameter and the order parameter of discrete fractional Hénon map to obtain the two discrete fractional Hénon maps in a synchronized regime and analyze the effect of linear coupling on synchronized degree. It demonstrates that the order parameter of discrete fractional Hénon map affects synchronization dynamics and with the increase of linear coupling strength, the effect of synchronization between discrete fractional Hénon maps is enhanced. Further investigation reveals that the transition of synchronization between discrete fractional Hénon maps are related to the critical changes in linearly coupled strength.

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