The fractional Potts model on diamond-like hierarchical lattices is introduced in this manuscript, which is a fractional rational system in the complex plane. Then, the fractal dynamics of this model is discussed from the fractal viewpoint. Julia set of the fractional Potts model is given, and control items of this fractional model are designed to control the Julia set. To associate two different Julia sets of the fractional model with different parameters and fractional orders, nonlinear coupling items are taken to make one Julia set change to another. The simulations are provided to illustrate the efficacy of these methods.

中文翻译：

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类菱形格上分形动力学和分数阶模型的控制

该手稿介绍了类菱形分层晶格上的分数波特模型，这是复杂平面上的分数有理系统。然后，从分形的角度讨论了该模型的分形动力学。给出了分数Potts模型的Julia集，并设计了该分数模型的控制项来控制Julia集。为了使分数模型的两个不同的Julia集与不同的参数和分数阶相关联，采用非线性耦合项将一个Julia集更改为另一个。提供模拟以说明这些方法的有效性。