%0 Journal Article
%T Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge
%A Uttam Das
%A T. K. Kar
%A U. K. Pahari
%J ISRN Biomathematics
%D 2013
%R 10.1155/2013/637640
%X This paper describes a prey-predator model with Holling type II functional response incorporating constant prey refuge and harvesting to both prey and predator species. We have analyzed the boundedness of the system and existence of all possible feasible equilibria and discussed local as well as global stabilities at interior equilibrium of the system. The occurrence of Hopf bifurcation of the system is examined, and it was observed that the bifurcation is either supercritical or subcritical. Influences of prey refuge and harvesting efforts are also discussed. Some numerical simulations are carried out for the validity of theoretical results. 1. Introduction Prey-predator models are of great interest to researchers in mathematics and ecology because they deal with environmental problems such as community¡¯s morbidity and how to control it and optimal harvest policy to sustain a community. In the physical sciences, generic models can be constructed to explain a variety of phenomena. However, in the life sciences, a model only describes a particular situation. So a variety of models are needed due to the complexity of the ecosystem. Theoretical and numerical studies of these models are able to give us an understanding of the interactions that are taking place. While investigating biological phenomena, there are many factors which affect dynamical properties of biological and mathematical models. One of the familiar nonlinear factors is the functional response. In population dynamics, a functional response of the predator to the prey density refers to the change in the density of prey attached per unit time per predator as the prey density changes [1]. Holling [2] suggested three different kinds of functional response for different kinds of species to model the phenomena of predation, which made the classical Lotka-Volterra system more realistic. The other factor which affects dynamical properties is harvesting. The subject of harvesting in predator-prey systems has been of interest to economists, ecologists, and natural resource managers for some time now. There are basically three types of harvesting reported in the literature: (i) constant harvesting where a constant number of individuals are harvested per unit time, (ii) proportional harvesting where the number of individuals harvested per unit time is proportional to the current population, and (iii) nonlinear harvesting. Most research has focused attention on optimal exploitation, guided entirely by profits from harvesting. First of all, depending on the nature of the applied harvesting strategy, the
%U http://www.hindawi.com/journals/isrn.biomathematics/2013/637640/