Abstract
Abstract In this paper, we consider a prey-predator model with a reserve region of predator where generalist predator cannot enter. Based on the intake capacity of food and other factors, we introduce the predator population which consumes the prey population with Holling type-II functional response; and generalist predator population consumes the predator population with Beddington-DeAngelis functional response. The density-dependent mortality rate for prey and generalist predator are considered. The equilibria of proposed system are determined. Local stability for the system are discussed. The environmental carrying capacity is considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighbourhood at an interior equilibrium point. Here the fishing effort is used as a control parameter to harvest the generalist predator population of the system. With the help of this control parameter, a dynamic framework is developed to investigate the optimal utilization of resources, sustainability properties of the stock and the resource rent. Finally, we present a numerical simulation to verify the analytical results, and the system is analyzed through graphical illustrations. The main findings with future research directions are described at last.
Highlights
Predation is an important factor in a food chain
Based on the intake capacity of food and other factors, we introduce the predator population which consumes the prey population with Holling type-II functional response; and generalist predator population consumes the predator population with Beddington-DeAngelis functional response
We have formulated the mathematical model on prey-predator relationship in a drainage basin
Summary
Predation is an important factor in a food chain. In predation, predators may or may not kill their prey prior to feeding on them, but the act of predation often results in the death of its prey through consumption. Abstract: In this paper, we consider a prey-predator model with a reserve region of predator where generalist predator cannot enter. The shing e ort is used as a control parameter to harvest the generalist predator population of the system. Researchers ([19],[20]) have shown their interest to study prey-predator system in a nature reserve region.
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