# American Institute of Mathematical Sciences

2014, 11(4): 823-839. doi: 10.3934/mbe.2014.11.823

## Coexistence and asymptotic stability in stage-structured predator-prey models

 1 Department of Mathematics and Statistics, UNC Wilmington, Wilmington, NC 28403 2 Mathematics and Statistics Department, University of North Carolina Wilmington, Wilmington, NC 28403-5970, United States, United States

Received  January 2013 Revised  August 2013 Published  March 2014

In this paper we analyze the effects of a stage-structured predator-prey system where the prey has two stages, juvenile and adult. Three different models (where the juvenile or adult prey populations are vulnerable) are studied to evaluate the impacts of this structure to the stability of the system and coexistence of the species. We assess how various ecological parameters, including predator mortality rate and handling times on prey, prey growth rate and death rate, prey capture rate and nutritional values in two stages, affect the existence and stability of all possible equilibria 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 equilibrium where both the predator and prey can co-exist Through specific examples, we demonstrate the stability of the trivial and co-existence equilibrium as well as the dynamics in each system.
Citation: Wei Feng, Michael T. Cowen, Xin Lu. Coexistence and asymptotic stability in stage-structured predator-prey models. Mathematical Biosciences & Engineering, 2014, 11 (4) : 823-839. doi: 10.3934/mbe.2014.11.823
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