Harvesting Strategies in the Migratory Prey-Predator Model with a Crowley-Martin Type Response Function and Constant Efforts

Abstract

This paper deals with the dynamics of prey and predator populationsin the permitted and prohibited areas of harvesting with a Crowley-Martin responsefunction. The predator can migrate easily into both areas. The prey and predatorpopulations in the permitted area are harvested with constant efforts. The existenceand stability of the interior equilibrium point are studied. The stable interior equilib?rium point is connected with maximum profit. The stability of the interior equilibriumpoint is analysed locally using the linearization method and eigenvalues. Due to thecomplexity, the simulation is carried out using the relevant parameter values to de?termine the existence of a stable interior equilibrium point and profit function. Fromsimulation, there exists an ordered pair of harvesting efforts that gives a stable in?terior equilibrium point and also maximizes the profit function. Harvesting in preyand predator populations in the permitted area can prevent the populations fromextinction and also provide maximum sustainable profit. The trajectories of prey andpredator populations are plotted to visualize the dynamical behaviour for a givenspan of time. The surface of profit function is also plotted to view the maximumprofit