Persistence and global stability of a Leslie-Gower predator-prey refuge system with a competitor for the prey

Chandan Maji, Debasis Mukherjee, Dipak Kesh

Abstract


This paper analyzes the effect of refuge on the dynamics of a Leslie-Gower predator-prey model in which one predator feeds on one of two competing species. Existence conditions for equilibrium points are discussed. By using differential inequality argument, we developed persistence criterion. Sufficient condition for global stability of the unique positive equilibrium point is derived. Different type of local bifurcation near the equilibrium points has been investigated. The role of refuges have been shown on equilibrium densities of prey, competitor for prey and predator respectively. The results establish the fact that the effects of refuges used by prey increase the equilibrium density of prey population under certain restrictions, whereas opposite hold for competitor of prey population. However equilibrium density of predator may decrease or increase by increasing the amount of prey refuge. Some numerical simulations are performed to validate the results obtained.

https://doi.org/10.28919/cmbn/3382


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Published: 2017-08-25

How to Cite this Article:

Chandan Maji, Debasis Mukherjee, Dipak Kesh, Persistence and global stability of a Leslie-Gower predator-prey refuge system with a competitor for the prey, Communications in Mathematical Biology and Neuroscience, Vol 2017 (2017), Article ID 19

Copyright © 2017 Chandan Maji, Debasis Mukherjee, Dipak Kesh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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