A three-dimensional (3D) Hénon map of fractional order is proposed in this paper. The dynamics of the suggested map are numerically illustrated for different fractional orders using phase plots and bifurcation diagrams. Lorenz-like attractors for the considered map are realized. Then, using the linear fractional-order systems stability criterion, a controller is proposed to globally stabilize the fractional-order Hénon map. Furthermore, synchronization control scheme has been designed to exhibit a synchronization behavior between a given 2D fractional-order chaotic map and the 3D fractional-order Hénon map. Numerical simulations are also performed to verify the main results of the study.

中文翻译：

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具有类洛伦兹吸引子的三维分数阶 Hénon 映射

本文提出了分数阶的三维 (3D) Hénon 图。使用相位图和分岔图对不同分数阶的建议映射的动态进行了数值说明。实现了所考虑地图的类洛伦兹吸引子。然后，使用线性分数阶系统稳定性判据，提出了一种全局稳定分数阶 Hénon 映射的控制器。此外，同步控制方案被设计为展示给定的 2D 分数阶混沌映射和 3D 分数阶 Hénon 映射之间的同步行为。还进行了数值模拟以验证研究的主要结果。