On a diffusive predator-prey model with nonlinear harvesting
In this paper, we study the dynamics of a diffusive Leslie-Gower model with a nonlinear harvesting term on the prey. We analyze the existence of positive equilibria and their dynamical behaviors. In particular, we consider the model with a weak harvesting term and find the conditions for the local a...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.807 |
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| _version_ | 1832590154500407296 |
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| author | Peng Feng |
| author_facet | Peng Feng |
| author_sort | Peng Feng |
| collection | DOAJ |
| description | In this paper, we study the dynamics of a diffusive Leslie-Gower model with a nonlinear harvesting term on the prey. We analyze the existence of positive equilibria and their dynamical behaviors. In particular, we consider the model with a weak harvesting term and find the conditions for the local and global asymptotic stability of the interior equilibrium. The global stability is established by considering a proper Lyapunov function. In contrast, the model with strong harvesting term has two interior equilibria and bi-stability may occur for this system. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns. |
| format | Article |
| id | doaj-art-dc1853852f2347de800d3575662f6a57 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-dc1853852f2347de800d3575662f6a572025-01-24T02:28:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-02-0111480782110.3934/mbe.2014.11.807On a diffusive predator-prey model with nonlinear harvestingPeng Feng0Department of Mathematics, Florida Gulf Coast University, 11501 FGCU Blvd. S., Fort Myers, FL 33965In this paper, we study the dynamics of a diffusive Leslie-Gower model with a nonlinear harvesting term on the prey. We analyze the existence of positive equilibria and their dynamical behaviors. In particular, we consider the model with a weak harvesting term and find the conditions for the local and global asymptotic stability of the interior equilibrium. The global stability is established by considering a proper Lyapunov function. In contrast, the model with strong harvesting term has two interior equilibria and bi-stability may occur for this system. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.807pattern formationglobal stability.turing instabilitynonlinear harvestingleslie-gowerpredator-prey |
| spellingShingle | Peng Feng On a diffusive predator-prey model with nonlinear harvesting Mathematical Biosciences and Engineering pattern formation global stability. turing instability nonlinear harvesting leslie-gower predator-prey |
| title | On a diffusive predator-prey model with nonlinear harvesting |
| title_full | On a diffusive predator-prey model with nonlinear harvesting |
| title_fullStr | On a diffusive predator-prey model with nonlinear harvesting |
| title_full_unstemmed | On a diffusive predator-prey model with nonlinear harvesting |
| title_short | On a diffusive predator-prey model with nonlinear harvesting |
| title_sort | on a diffusive predator prey model with nonlinear harvesting |
| topic | pattern formation global stability. turing instability nonlinear harvesting leslie-gower predator-prey |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.807 |
| work_keys_str_mv | AT pengfeng onadiffusivepredatorpreymodelwithnonlinearharvesting |