Approximate analysis of population dynamics with density-dependent migrations and the Allee effects

Purpose - The aim of this paper is to present the numerical simulation of the population dynamics model with density-dependent migrations and the Allee effects using the homotopy perturbation method (HPM). Design/methodology/ approach - The paper applied HPM and the results obtained by this method are compared to the exact solution. The results show applicability, accuracy and efficiency of HPM in solving the transient non-linear advection-diffusion- reaction equation. Findings - In this study, HPM is applied to solve the model of population dynamics with density- dependent migrations and the Allee effects. Numerical approximations show a high degree of accuracy. The numerical results we obtained justify the advantage of this methodology, even in the few terms approximation is accurate. Errors can be made smaller by taking new terms of the iteration formulas. Originality/value - It is confirmed that the work has not been published in any other journal. © 2012 Emerald Group Publishing Limited.