Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations
We have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted as L must be greater than the critical patch...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/485860 |
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| author | Kolade M. Owolabi Kailash C. Patidar |
| author_facet | Kolade M. Owolabi Kailash C. Patidar |
| author_sort | Kolade M. Owolabi |
| collection | DOAJ |
| description | We have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted as L must be greater than the critical patch size Lc. It was also observed that the reaction-diffusion problem can be split into two parts: the linear and nonlinear terms. Hence, the use of two classical methods in space and time is permitted. We use spectral method in the area of mathematical community to remove the stiffness associated with the linear or diffusive terms. The resulting system is advanced with a modified exponential time-differencing method whose formulation was based on the fourth-order Runge-Kutta scheme. With high-order method, this extends the one-dimensional work and presents experiments for two-dimensional problem. The complexity of the dynamical model is discussed theoretically and graphically simulated to demonstrate and compare the behavior of the time-dependent density function. |
| format | Article |
| id | doaj-art-ea686012ae9f414d8eb54dbed2c17d1f |
| institution | OA Journals |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-ea686012ae9f414d8eb54dbed2c17d1f2025-08-20T02:21:54ZengWileyInternational Journal of Differential Equations1687-96431687-96512015-01-01201510.1155/2015/485860485860Existence and Permanence in a Diffusive KiSS Model with Robust Numerical SimulationsKolade M. Owolabi0Kailash C. Patidar1Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South AfricaDepartment of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South AfricaWe have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted as L must be greater than the critical patch size Lc. It was also observed that the reaction-diffusion problem can be split into two parts: the linear and nonlinear terms. Hence, the use of two classical methods in space and time is permitted. We use spectral method in the area of mathematical community to remove the stiffness associated with the linear or diffusive terms. The resulting system is advanced with a modified exponential time-differencing method whose formulation was based on the fourth-order Runge-Kutta scheme. With high-order method, this extends the one-dimensional work and presents experiments for two-dimensional problem. The complexity of the dynamical model is discussed theoretically and graphically simulated to demonstrate and compare the behavior of the time-dependent density function.http://dx.doi.org/10.1155/2015/485860 |
| spellingShingle | Kolade M. Owolabi Kailash C. Patidar Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations International Journal of Differential Equations |
| title | Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations |
| title_full | Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations |
| title_fullStr | Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations |
| title_full_unstemmed | Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations |
| title_short | Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations |
| title_sort | existence and permanence in a diffusive kiss model with robust numerical simulations |
| url | http://dx.doi.org/10.1155/2015/485860 |
| work_keys_str_mv | AT kolademowolabi existenceandpermanenceinadiffusivekissmodelwithrobustnumericalsimulations AT kailashcpatidar existenceandpermanenceinadiffusivekissmodelwithrobustnumericalsimulations |