Dynamical behaviour of age-selective harvesting of a prey-predator system

Abstract

In this article we have discussed the dynamical behaviour of a harvested prey-predator fish population with time delay in the prey harvesting term as well as in the predator harvesting term. Thus we are considering selective harvesting of both species. Biologically it implies that we are allowing both prey and predator populations to elapse some fixed time before they are harvested. In other words, we are restricting harvesting of species below some certain age so that they can grow up to some specific size or age and thus protecting juvenile fish. Age-selective harvesting, where the old individuals of a particular species are preferentially taken, is common in both ecosystem-based fisheries and forestry management. Depending upon the age selection strategy, system experiences stable coexistence to oscillatory mode and vice versa via Hopf-bifurcation. Our analysis supports that balance between harvesting delays and harvesting intensities should be maintained for better ecosystem management. All our important findings are numerically verified using MATLAB.