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Dynamics of a prey-predator model with reserve area for prey and modified effort function

Y. Louartassi, M. R. Lemnaouar, H. Benazza, M. Khalfaoui

Abstract



In this paper, we propose and analyze a nonlinear mathematical model to study the dynamics of a resource fishery in an aquatic environment composed of two zones: a free fishing zone and a reserve zone where fishing is strictly forbidden (See (Kar., 2006)). A modified effort function E is considered which depends on the density effect of the fish population (See (Ideals and Wang, 1964)). The biological equilibria of the system are obtained as well
as the criteria of local stability and global stability. Finally, numerical simulations are carried to verify the theoretical conclusions.

Keywords


Prey-predator system, Equilibria, Stability, modified function.

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