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
Highlights
There has been a growing interest in the study of refuges in predator-prey system
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
Kar [9] investigated a Lotka-Volterra type predator-prey system incorporating a constant proportion of prey refuges with Holling type-II response function
Summary
There has been a growing interest in the study of refuges in predator-prey system. Gonzalez-. Kar [9] investigated a Lotka-Volterra type predator-prey system incorporating a constant proportion of prey refuges with Holling type-II response function. He remarked that it is possible to break the cyclic behaviour of the system if harvesting effects as controls. Mukherjee [14] studied the effect of immigration and refuge on the dynamics of three species system He discussed about the persistence of the system and global stability. In another paper [16] Mukherjee investigated same type of situation without immigration and predation process follows Holling-type II response function Both of the papers, he did not addressed what will be dynamical consequence if Leslie-Gower form is taken.
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