Laplace transform-homotopy perturbation method for fractional time diffusive predator–prey models in ecology

Abstract

In this paper, we consider some reaction–diffusion systems arising from two-component predator–prey models with various kinetics ranging from prey-dependent, ratio-dependent functional responses and subdiffusion. The goal of the present work is to simulate the time-dependent predator–prey model of Lotka–Volterra. Analytical solutions of this model are performed using the Laplace transform-homotopy perturbation method. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that the proposed technique solves nonlinear problems without using Adomian’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method. We show all the possible equilibria and examine their stability in line with the ecological parameters. Numerical simulations of the diffusive predator–prey model in one-, two- and three-dimensions are given to compare and demonstrate the asymptotic behaviour of the time-dependent reaction–diffusion systems. The results show that proposed technique is a powerful tool to solve systems of nonlinear ordinary and partial differential equations of predator–prey models in ecology.

Keywords

• Subdiffusive predator–prey models
• Linear stability analysis
• Homotopy perturbation method
• Simulations in 1D-2D