Computational dynamics of predator-prey model with the power-law kernel
Evolution system which contains fractional derivatives can give rise to useful mathematical model for describing some important real-life or physical scenarios. Here, we suggest some numerical techniques for solving fractional-in-time reaction-diffusion models in the sense of Caputo operator. The su...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-02-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379720322130 |
| _version_ | 1818870550260350976 |
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| author | Kolade M. Owolabi |
| author_facet | Kolade M. Owolabi |
| author_sort | Kolade M. Owolabi |
| collection | DOAJ |
| description | Evolution system which contains fractional derivatives can give rise to useful mathematical model for describing some important real-life or physical scenarios. Here, we suggest some numerical techniques for solving fractional-in-time reaction-diffusion models in the sense of Caputo operator. The suggested schemes are formulated with difference scheme and Fourier-spectral algorithm. In the simulation framework, it was observed that the spectral method retains the advantage of spectral accuracy over its finite difference counterpart. Both techniques are easy to adapt and extend to high-dimensions in space and time. The existence of solution, uniqueness of solution, linear stability analysis as well as the calculation of the Lyapunov exponent of the main system, are well established. Suitability of the suggested numerical techniques are tested on non-diffusive model, one-dimensional diffusive example and two-dimensional diffusive experiments. |
| first_indexed | 2024-12-19T12:08:48Z |
| format | Article |
| id | doaj.art-8f206aed97f544d793a479eca642d0b3 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-19T12:08:48Z |
| publishDate | 2021-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-8f206aed97f544d793a479eca642d0b32022-12-21T20:22:16ZengElsevierResults in Physics2211-37972021-02-0121103810Computational dynamics of predator-prey model with the power-law kernelKolade M. Owolabi0Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa; Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria; Address: Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria.Evolution system which contains fractional derivatives can give rise to useful mathematical model for describing some important real-life or physical scenarios. Here, we suggest some numerical techniques for solving fractional-in-time reaction-diffusion models in the sense of Caputo operator. The suggested schemes are formulated with difference scheme and Fourier-spectral algorithm. In the simulation framework, it was observed that the spectral method retains the advantage of spectral accuracy over its finite difference counterpart. Both techniques are easy to adapt and extend to high-dimensions in space and time. The existence of solution, uniqueness of solution, linear stability analysis as well as the calculation of the Lyapunov exponent of the main system, are well established. Suitability of the suggested numerical techniques are tested on non-diffusive model, one-dimensional diffusive example and two-dimensional diffusive experiments.http://www.sciencedirect.com/science/article/pii/S221137972032213034A3435K5765M0665L05 |
| spellingShingle | Kolade M. Owolabi Computational dynamics of predator-prey model with the power-law kernel Results in Physics 34A34 35K57 65M06 65L05 |
| title | Computational dynamics of predator-prey model with the power-law kernel |
| title_full | Computational dynamics of predator-prey model with the power-law kernel |
| title_fullStr | Computational dynamics of predator-prey model with the power-law kernel |
| title_full_unstemmed | Computational dynamics of predator-prey model with the power-law kernel |
| title_short | Computational dynamics of predator-prey model with the power-law kernel |
| title_sort | computational dynamics of predator prey model with the power law kernel |
| topic | 34A34 35K57 65M06 65L05 |
| url | http://www.sciencedirect.com/science/article/pii/S2211379720322130 |
| work_keys_str_mv | AT kolademowolabi computationaldynamicsofpredatorpreymodelwiththepowerlawkernel |