The aim of this paper is to analyze the chaotic dynamics of a novel 2D fractional order discrete Ushiki map using Caputo-like delta fractional difference operator. The dynamical nature of the proposed discrete fractional Ushiki map is examined with evolution of time states and bifurcation diagrams. In addition, control law aimed at stabilizing the proposed map and the synchronization of the discrete fractional order Ushiki map are also presented. Numerical examples are exhibited to demonstrate the validity of the theoretical findings of the study.

中文翻译：

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新型二维离散分数阶 USHIKI MAP 的混沌动力学

本文的目的是使用类似 Caputo 的 delta 分数差分算子来分析一种新颖的 2D 分数阶离散 Ushiki 映射的混沌动力学。通过时间状态和分岔图的演变来检查所提出的离散分数牛木图的动态特性。此外，还提出了旨在稳定所提出地图的控制律和离散分数阶牛木地图的同步。展示了数值示例以证明该研究的理论结果的有效性。