Bioeconomic modelling of a prey predator system using differential algebraic equations

Abstract

We propose a biological economic model based on prey-predator dynamics where the prey species are continuously harvested and predation is considered with type II functional response. The dynamic behavior of the proposed biological economic preypredator model is discussed. Continuous type gestational delay of predators is incorporated and its effect on the dynamical behavior of the model system is analyzed. Through considering delay as a bifurcation parameter, the occurrence of Hopf bifurcation of the proposed model system with positive economic profit is shown in the neighborhood of the co-existing equilibrium point. Finally, some numerical simulations are given to verify the analytical results and the system is analyzed through graphical illustrations.

Keywords: Bioeconomics, differential algebraic system, time delay, Hopf bifurcation