Abstract
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.
Highlights
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
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]
This paper deals with a prey-predator model with Holling type II functional response incorporating a constant prey refuge and independent harvesting in either species
Summary
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. Effects of harvesting on various types of prey-predator models have been considered by many researchers. Kar [12] proposed a predator-prey model incorporating a prey refuge and independent harvesting on either species. He showed that, using the harvesting efforts as control, it is possible to break the cyclic behavior of the system. The objective of this paper is to study the combined effects of harvesting and constant prey refuge on the dynamics of predator-prey model. And studied instability and global stability of the equilibria and uniqueness of limit cycle and showed the influence of constant prey refuge and constant-rate prey harvesting.
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