Novel Patterns in Fractional-in-Space Nonlinear Coupled FitzHugh–Nagumo Models with Riesz Fractional Derivative
In this paper, the Fourier spectral method is used to solve the fractional-in-space nonlinear coupled FitzHugh–Nagumo model.Numerical simulation is carried out to elucidate the diffusion behavior of patterns for the fractional 2D and 3D FitzHugh–Nagumo model. The results of numerical experiments are...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/3/136 |
| _version_ | 1797471546831273984 |
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| author | Xiaoyu Li Che Han Yulan Wang |
| author_facet | Xiaoyu Li Che Han Yulan Wang |
| author_sort | Xiaoyu Li |
| collection | DOAJ |
| description | In this paper, the Fourier spectral method is used to solve the fractional-in-space nonlinear coupled FitzHugh–Nagumo model.Numerical simulation is carried out to elucidate the diffusion behavior of patterns for the fractional 2D and 3D FitzHugh–Nagumo model. The results of numerical experiments are consistent with the theoretical results of other scholars, which verifies the accuracy of the method. We show that stable spatio-temporal patterns can be sustained for a long time; these patterns are different from any previously obtained in numerical studies. Here, we show that behavior patterns can be described well by the fractional FitzHugh–Nagumo and Gray–Scott models, which have unique properties that integer models do not have. Results show that the Fourier spectral method has strong competitiveness, reliability, and solving ability for solving 2D and 3D fractional-in-space nonlinear reaction-diffusion models. |
| first_indexed | 2024-03-09T19:49:44Z |
| format | Article |
| id | doaj.art-e68c6d499885433db0e3dfe9c97ade59 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:49:44Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e68c6d499885433db0e3dfe9c97ade592023-11-24T01:14:14ZengMDPI AGFractal and Fractional2504-31102022-02-016313610.3390/fractalfract6030136Novel Patterns in Fractional-in-Space Nonlinear Coupled FitzHugh–Nagumo Models with Riesz Fractional DerivativeXiaoyu Li0Che Han1Yulan Wang2College of Science, Inner Mongolia University of Technology, Hohhot 010051, ChinaCollege of Science, Inner Mongolia University of Technology, Hohhot 010051, ChinaCollege of Science, Inner Mongolia University of Technology, Hohhot 010051, ChinaIn this paper, the Fourier spectral method is used to solve the fractional-in-space nonlinear coupled FitzHugh–Nagumo model.Numerical simulation is carried out to elucidate the diffusion behavior of patterns for the fractional 2D and 3D FitzHugh–Nagumo model. The results of numerical experiments are consistent with the theoretical results of other scholars, which verifies the accuracy of the method. We show that stable spatio-temporal patterns can be sustained for a long time; these patterns are different from any previously obtained in numerical studies. Here, we show that behavior patterns can be described well by the fractional FitzHugh–Nagumo and Gray–Scott models, which have unique properties that integer models do not have. Results show that the Fourier spectral method has strong competitiveness, reliability, and solving ability for solving 2D and 3D fractional-in-space nonlinear reaction-diffusion models.https://www.mdpi.com/2504-3110/6/3/136Riesz fractional derivativeFitzHugh–Nagumo modelspatial patternsFourier spectral method |
| spellingShingle | Xiaoyu Li Che Han Yulan Wang Novel Patterns in Fractional-in-Space Nonlinear Coupled FitzHugh–Nagumo Models with Riesz Fractional Derivative Fractal and Fractional Riesz fractional derivative FitzHugh–Nagumo model spatial patterns Fourier spectral method |
| title | Novel Patterns in Fractional-in-Space Nonlinear Coupled FitzHugh–Nagumo Models with Riesz Fractional Derivative |
| title_full | Novel Patterns in Fractional-in-Space Nonlinear Coupled FitzHugh–Nagumo Models with Riesz Fractional Derivative |
| title_fullStr | Novel Patterns in Fractional-in-Space Nonlinear Coupled FitzHugh–Nagumo Models with Riesz Fractional Derivative |
| title_full_unstemmed | Novel Patterns in Fractional-in-Space Nonlinear Coupled FitzHugh–Nagumo Models with Riesz Fractional Derivative |
| title_short | Novel Patterns in Fractional-in-Space Nonlinear Coupled FitzHugh–Nagumo Models with Riesz Fractional Derivative |
| title_sort | novel patterns in fractional in space nonlinear coupled fitzhugh nagumo models with riesz fractional derivative |
| topic | Riesz fractional derivative FitzHugh–Nagumo model spatial patterns Fourier spectral method |
| url | https://www.mdpi.com/2504-3110/6/3/136 |
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