A Fractional Order Bazykin’s Predator–Prey System and its Solution

Abstract

This paper addresses Bazykin’s prey predator system, which is an ecological model comprising two differential equations for prey and predator species including predator intra-species competition. We study the solution of Bazykin’s predator–prey model of fractional order utilizing the Homotopy Perturbation Method (HPM). Here, the fractional order Bazykin’s model is developed from the integer order counterpart. Additionally, the Holling type-II response function is included in Bazykin’s model, which we have approximated employing Taylor’s polynomial in order to utilise HPM. Extensive numerical simulations are performed for various scenarios. Our numerical findings suggest that few terms of the series solution yield a precise approximate solution. Discussion is held regarding the solutions’ dependence on fractional orders. This method is highly efficient as well as straightforward in analysing this ecological system.