A Multi-Stage Homotopy Perturbation Method for the Fractional Lotka-Volterra Model

Abstract

In this work, we propose an efficient multi-stage homotopy perturbation method to find an analytic solution to the fractional Lotka-Volterra model. We obtain its order of accuracy, and we study the stability of the system. Moreover, we present several examples to show of the effectiveness of this method, and we conclude that the value of the derivative order plays an important role in the trajectories velocity.

Keywords

• predator-prey model
• anomalous dynamical system
• caputo fractional derivative