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

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

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 contr...

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Main Authors: Weihua Sun, Shutang Liu
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/8547685
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spelling doaj-fd44b189cf004b3f9d76c268532a2e512020-11-25T03:29:20ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/85476858547685Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical LatticesWeihua Sun0Shutang Liu1School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, ChinaSchool of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, ChinaThe 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.http://dx.doi.org/10.1155/2020/8547685
collection DOAJ
language English
format Article
sources DOAJ
author Weihua Sun
Shutang Liu
spellingShingle Weihua Sun
Shutang Liu
Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
Discrete Dynamics in Nature and Society
author_facet Weihua Sun
Shutang Liu
author_sort Weihua Sun
title Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
title_short Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
title_full Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
title_fullStr Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
title_full_unstemmed Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
title_sort fractal dynamics and control of the fractional potts model on diamond-like hierarchical lattices
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2020-01-01
description 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.
url http://dx.doi.org/10.1155/2020/8547685
work_keys_str_mv AT weihuasun fractaldynamicsandcontrolofthefractionalpottsmodelondiamondlikehierarchicallattices
AT shutangliu fractaldynamicsandcontrolofthefractionalpottsmodelondiamondlikehierarchicallattices
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