Fractional Lotka–Volterra model with Holling type III functional response

Abstract

In this paper, we study a generalization of a Lotka–Volterra system with Holling type III functional response, where the Caputo fractional derivative is considered. Applying a multistage homotopy perturbation method, we obtain an analytical solution for the system. Moreover, analyzing the eigenvalues of the Jacobian matrix around the equilibria, we find sufficient conditions in order to guarantee the local stability and we present several examples to illustrate the behavior of solutions.