Coexistence and asymptotic stability in stage-structured predator-prey models
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Department of Mathematics and Statistics, UNC Wilmington, Wilmington, NC 28403
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Mathematics and Statistics Department, University of North Carolina Wilmington, Wilmington, NC 28403-5970
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Received:
01 January 2013
Accepted:
29 June 2018
Published:
01 March 2014
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MSC :
Primary: 34A34, 34C11, 34D20, 34D23; Secondary: 92D25.
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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.
Citation: Wei Feng, Michael T. Cowen, Xin Lu. Coexistence and asymptotic stability in stage-structured predator-prey models[J]. Mathematical Biosciences and Engineering, 2014, 11(4): 823-839. doi: 10.3934/mbe.2014.11.823
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Abstract
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.
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