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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/8547685 |
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| _version_ | 1832560360061665280 |
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| author | Weihua Sun Shutang Liu |
| author_facet | Weihua Sun Shutang Liu |
| author_sort | Weihua Sun |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-fd44b189cf004b3f9d76c268532a2e51 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fd44b189cf004b3f9d76c268532a2e512025-02-03T01:27:56ZengWileyDiscrete 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2020/8547685 |
| work_keys_str_mv | AT weihuasun fractaldynamicsandcontrolofthefractionalpottsmodelondiamondlikehierarchicallattices AT shutangliu fractaldynamicsandcontrolofthefractionalpottsmodelondiamondlikehierarchicallattices |