Abstract
In this paper, according to the knowledge of discrete fractional calculus and quantum game chaotic map, we first get the fractional quantum game chaotic map, which describes the dynamics of a quantum duopoly game. Then, the phase space, maximum Lyapunov exponent, and bifurcation diagram of the proposed map are obtained for the purpose of observing dynamic behaviors compared with the original quantum game chaotic map. After that, the synchronous controller is designed and the chaos synchronization of the fractional quantum game chaotic map is observed. Finally, we develop the fractional quantum game chaotic map into the chaotic sequence generator and image encryption scheme.
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