Coexistence and asymptotic stability in stage-structured predator-prey models
In this paper we analyze the effects of a stage-structuredpredator-prey system where the prey has two stages, juvenile andadult. Three different models (where the juvenile or adult preypopulations are vulnerable) are studied to evaluate the impacts ofthis structure to the stability of the system and...
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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.2014.11.823 |
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| author | Wei Feng Michael T. Cowen Xin Lu |
| author_facet | Wei Feng Michael T. Cowen Xin Lu |
| author_sort | Wei Feng |
| collection | DOAJ |
| description | In this paper we analyze the effects of a stage-structuredpredator-prey system where the prey has two stages, juvenile andadult. Three different models (where the juvenile or adult preypopulations are vulnerable) are studied to evaluate the impacts ofthis structure to the stability of the system and coexistence of thespecies. We assess how various ecological parameters, includingpredator mortality rate and handling times on prey, prey growth rateand death rate, prey capture rate and nutritional valuesin two stages, affect the existence and stability of all possibleequilibria in each of the models, as well as the ultimate bounds and the dynamics of the populations.The main focus of this paper is to find general conditions to ensure the presence and stability of the coexistence equilibriumwhere both the predator and prey can co-existThrough specific examples, we demonstrate thestability of the trivial and co-existence equilibrium as well as the dynamics in eachsystem. |
| format | Article |
| id | doaj-art-667e581483644f07934a6cb8f6c2dff4 |
| 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-667e581483644f07934a6cb8f6c2dff42025-01-24T02:28:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-02-0111482383910.3934/mbe.2014.11.823Coexistence and asymptotic stability in stage-structured predator-prey modelsWei Feng0Michael T. Cowen1Xin Lu2Department of Mathematics and Statistics, UNC Wilmington, Wilmington, NC 28403Mathematics and Statistics Department, University of North Carolina Wilmington, Wilmington, NC 28403-5970Mathematics and Statistics Department, University of North Carolina Wilmington, Wilmington, NC 28403-5970In this paper we analyze the effects of a stage-structuredpredator-prey system where the prey has two stages, juvenile andadult. Three different models (where the juvenile or adult preypopulations are vulnerable) are studied to evaluate the impacts ofthis structure to the stability of the system and coexistence of thespecies. We assess how various ecological parameters, includingpredator mortality rate and handling times on prey, prey growth rateand death rate, prey capture rate and nutritional valuesin two stages, affect the existence and stability of all possibleequilibria in each of the models, as well as the ultimate bounds and the dynamics of the populations.The main focus of this paper is to find general conditions to ensure the presence and stability of the coexistence equilibriumwhere both the predator and prey can co-existThrough specific examples, we demonstrate thestability of the trivial and co-existence equilibrium as well as the dynamics in eachsystem.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.823stability analysisstage-structured modelspredator-prey interactionscoexistence and simulations. |
| spellingShingle | Wei Feng Michael T. Cowen Xin Lu Coexistence and asymptotic stability in stage-structured predator-prey models Mathematical Biosciences and Engineering stability analysis stage-structured models predator-prey interactions coexistence and simulations. |
| title | Coexistence and asymptotic stability in stage-structured predator-prey models |
| title_full | Coexistence and asymptotic stability in stage-structured predator-prey models |
| title_fullStr | Coexistence and asymptotic stability in stage-structured predator-prey models |
| title_full_unstemmed | Coexistence and asymptotic stability in stage-structured predator-prey models |
| title_short | Coexistence and asymptotic stability in stage-structured predator-prey models |
| title_sort | coexistence and asymptotic stability in stage structured predator prey models |
| topic | stability analysis stage-structured models predator-prey interactions coexistence and simulations. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.823 |
| work_keys_str_mv | AT weifeng coexistenceandasymptoticstabilityinstagestructuredpredatorpreymodels AT michaeltcowen coexistenceandasymptoticstabilityinstagestructuredpredatorpreymodels AT xinlu coexistenceandasymptoticstabilityinstagestructuredpredatorpreymodels |