Spatiotemporal complexity in a predator--prey model with weak Allee effects
In this article, we study the rich dynamics of a diffusive predator-prey system with Allee effects in the prey growth. Our model assumes a prey-dependent Holling type-II functional response and a density dependent death rate for predator. We investigate the dissipation and persistence property, the...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2014-08-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1247 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590148506746880 |
|---|---|
| author | Yongli Cai Malay Banerjee Yun Kang Weiming Wang |
| author_facet | Yongli Cai Malay Banerjee Yun Kang Weiming Wang |
| author_sort | Yongli Cai |
| collection | DOAJ |
| description | In this article, we study the rich dynamics of a diffusive predator-prey system with Allee effects in the prey growth. Our model assumes a prey-dependent Holling type-II functional response and a density dependent death rate for predator. We investigate the dissipation and persistence property, the stability of nonnegative and positive constant steady state of the model, as well as the existence of Hopf bifurcation at the positive constant solution. In addition, we provide results on the existence and non-existence of positive non-constant solutions of the model. We also demonstrate the Turing instability under some conditions, and find that our model exhibits a diffusion-controlled formation growth of spots, stripes, and holes pattern replication via numerical simulations. One of the most interesting findings is that Turing instability in the model is induced by the density dependent death rate in predator. |
| format | Article |
| id | doaj-art-c713a4562e6e433a806e7dc041f242e5 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c713a4562e6e433a806e7dc041f242e52025-01-24T02:29:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-08-011161247127410.3934/mbe.2014.11.1247Spatiotemporal complexity in a predator--prey model with weak Allee effectsYongli Cai0Malay Banerjee1Yun Kang2Weiming Wang3Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, Uttar PradeshScience and Mathematics Faculty, School of Letters and Sciences, Arizona State University, Mesa, AZ 85212College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035In this article, we study the rich dynamics of a diffusive predator-prey system with Allee effects in the prey growth. Our model assumes a prey-dependent Holling type-II functional response and a density dependent death rate for predator. We investigate the dissipation and persistence property, the stability of nonnegative and positive constant steady state of the model, as well as the existence of Hopf bifurcation at the positive constant solution. In addition, we provide results on the existence and non-existence of positive non-constant solutions of the model. We also demonstrate the Turing instability under some conditions, and find that our model exhibits a diffusion-controlled formation growth of spots, stripes, and holes pattern replication via numerical simulations. One of the most interesting findings is that Turing instability in the model is induced by the density dependent death rate in predator.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1247non-constant solutionturing instabilityallee effectspattern formation.density dependent |
| spellingShingle | Yongli Cai Malay Banerjee Yun Kang Weiming Wang Spatiotemporal complexity in a predator--prey model with weak Allee effects Mathematical Biosciences and Engineering non-constant solution turing instability allee effects pattern formation. density dependent |
| title | Spatiotemporal complexity in a predator--prey model with weak Allee effects |
| title_full | Spatiotemporal complexity in a predator--prey model with weak Allee effects |
| title_fullStr | Spatiotemporal complexity in a predator--prey model with weak Allee effects |
| title_full_unstemmed | Spatiotemporal complexity in a predator--prey model with weak Allee effects |
| title_short | Spatiotemporal complexity in a predator--prey model with weak Allee effects |
| title_sort | spatiotemporal complexity in a predator prey model with weak allee effects |
| topic | non-constant solution turing instability allee effects pattern formation. density dependent |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1247 |
| work_keys_str_mv | AT yonglicai spatiotemporalcomplexityinapredatorpreymodelwithweakalleeeffects AT malaybanerjee spatiotemporalcomplexityinapredatorpreymodelwithweakalleeeffects AT yunkang spatiotemporalcomplexityinapredatorpreymodelwithweakalleeeffects AT weimingwang spatiotemporalcomplexityinapredatorpreymodelwithweakalleeeffects |