Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis
In the realm of ecology, species naturally strive to enhance their own survival odds. This study introduces and investigates a predator-prey model incorporating reaction-diffusion through a system of differential equations. We scrutinize how diffusion impacts the model’s stability. By analysing the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2023/9190167 |
| _version_ | 1797657951897387008 |
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| author | N. B. Sharmila C. Gunasundari Mohammad Sajid |
| author_facet | N. B. Sharmila C. Gunasundari Mohammad Sajid |
| author_sort | N. B. Sharmila |
| collection | DOAJ |
| description | In the realm of ecology, species naturally strive to enhance their own survival odds. This study introduces and investigates a predator-prey model incorporating reaction-diffusion through a system of differential equations. We scrutinize how diffusion impacts the model’s stability. By analysing the stability of the model’s uniform equilibrium state, we identify a condition leading to Turing instability. The study delves into how diffusion influences pattern formation within a predator-prey system. Our findings reveal that various spatiotemporal patterns, such as patches, spots, and even chaos, emerge based on species diffusion rates. We derive the amplitude equation by employing the weak nonlinear multiple scales analysis technique and the Taylor series expansion. A novel sinc interpolation approach is introduced. Numerical simulations elucidate the interplay between diffusion and Turing parameters. In a two-dimensional domain, spatial pattern analysis illustrates population density dynamics resulting in isolated groups, spots, stripes, or labyrinthine patterns. Simulation results underscore the method’s effectiveness. The article concludes by discussing the biological implications of these outcomes. |
| first_indexed | 2024-03-11T17:53:08Z |
| format | Article |
| id | doaj.art-6e5420f18a3045d38e77535d806fdca1 |
| institution | Directory Open Access Journal |
| issn | 1687-9651 |
| language | English |
| last_indexed | 2024-03-11T17:53:08Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj.art-6e5420f18a3045d38e77535d806fdca12023-10-18T00:00:02ZengHindawi LimitedInternational Journal of Differential Equations1687-96512023-01-01202310.1155/2023/9190167Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear AnalysisN. B. Sharmila0C. Gunasundari1Mohammad Sajid2Department of MathematicsDepartment of MathematicsDepartment of Mechanical EngineeringIn the realm of ecology, species naturally strive to enhance their own survival odds. This study introduces and investigates a predator-prey model incorporating reaction-diffusion through a system of differential equations. We scrutinize how diffusion impacts the model’s stability. By analysing the stability of the model’s uniform equilibrium state, we identify a condition leading to Turing instability. The study delves into how diffusion influences pattern formation within a predator-prey system. Our findings reveal that various spatiotemporal patterns, such as patches, spots, and even chaos, emerge based on species diffusion rates. We derive the amplitude equation by employing the weak nonlinear multiple scales analysis technique and the Taylor series expansion. A novel sinc interpolation approach is introduced. Numerical simulations elucidate the interplay between diffusion and Turing parameters. In a two-dimensional domain, spatial pattern analysis illustrates population density dynamics resulting in isolated groups, spots, stripes, or labyrinthine patterns. Simulation results underscore the method’s effectiveness. The article concludes by discussing the biological implications of these outcomes.http://dx.doi.org/10.1155/2023/9190167 |
| spellingShingle | N. B. Sharmila C. Gunasundari Mohammad Sajid Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis International Journal of Differential Equations |
| title | Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis |
| title_full | Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis |
| title_fullStr | Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis |
| title_full_unstemmed | Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis |
| title_short | Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis |
| title_sort | spatiotemporal dynamics of a reaction diffusive predator prey model a weak nonlinear analysis |
| url | http://dx.doi.org/10.1155/2023/9190167 |
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