Modeling and analysis of a fractional-order prey-predator system incorporating harvesting

Abstract

In the present paper, we propose and study a fractional-order prey-predator type ecological model with the functional response of Holling type II and the effect of harvesting. In addition, we have also considered the influence of a super-predator on the conventional predator. The complex dynamical behaviour of the proposed model system including existence and uniqueness criteria, finiteness and nonnegativity of the solutions have studied rigorously. In addition, we have determined existence criteria of several equilibria and analyzed the asymptotic nature of those equilibria. We have enriched our analysis with the inclusion of fractional Hopf bifurcation and the criteria of global stability of the equilibrium points. Finally, some numerical simulation works have been incorporated to validate the analytical analysis.