Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect
We investigate a diffusive Leslie-Gower predator-prey model with the additive Allee effect on prey subject to the zero-flux boundary conditions. Some results of solutions to this model and its corresponding steady-state problem are shown. More precisely, we give the stability of the positive constan...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/535746 |
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| _version_ | 1849306482466619392 |
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| author | Yongli Cai Caidi Zhao Weiming Wang |
| author_facet | Yongli Cai Caidi Zhao Weiming Wang |
| author_sort | Yongli Cai |
| collection | DOAJ |
| description | We investigate a diffusive Leslie-Gower predator-prey model with the additive Allee effect on prey subject to the zero-flux boundary conditions. Some results of solutions to this model and its corresponding steady-state problem are shown. More precisely, we give the
stability of the positive constant steady-state solution, the refined a priori estimates of positive solution, and the nonexistence and existence of the positive nonconstant solutions. We carry out the analytical study for two-dimensional system in detail and find out the certain conditions for Turing instability. Furthermore, we perform numerical simulations and show that the model exhibits a transition from stripe-spot mixtures growth to isolated spots and
also to stripes. These results show that the impact of the Allee effect essentially increases the model spatiotemporal complexity. |
| format | Article |
| id | doaj-art-32375ef277b64e7490cc9b8870b8aade |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-32375ef277b64e7490cc9b8870b8aade2025-08-20T03:55:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/535746535746Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee EffectYongli Cai0Caidi Zhao1Weiming Wang2School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaWe investigate a diffusive Leslie-Gower predator-prey model with the additive Allee effect on prey subject to the zero-flux boundary conditions. Some results of solutions to this model and its corresponding steady-state problem are shown. More precisely, we give the stability of the positive constant steady-state solution, the refined a priori estimates of positive solution, and the nonexistence and existence of the positive nonconstant solutions. We carry out the analytical study for two-dimensional system in detail and find out the certain conditions for Turing instability. Furthermore, we perform numerical simulations and show that the model exhibits a transition from stripe-spot mixtures growth to isolated spots and also to stripes. These results show that the impact of the Allee effect essentially increases the model spatiotemporal complexity.http://dx.doi.org/10.1155/2013/535746 |
| spellingShingle | Yongli Cai Caidi Zhao Weiming Wang Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect Journal of Applied Mathematics |
| title | Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect |
| title_full | Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect |
| title_fullStr | Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect |
| title_full_unstemmed | Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect |
| title_short | Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect |
| title_sort | spatiotemporal complexity of a leslie gower predator prey model with the weak allee effect |
| url | http://dx.doi.org/10.1155/2013/535746 |
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