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Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices

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  • Weihua Sun
  • Shutang Liu

Abstract

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.

Suggested Citation

  • Weihua Sun & Shutang Liu, 2020. "Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-8, July.
    • Handle: RePEc:hin:jnddns:8547685
    DOI: 10.1155/2020/8547685
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