On Some Perturbation Approaches to Population Dynamics

TL;DR

This paper critically evaluates several perturbation methods and demonstrates their failure to accurately model the dynamics of a basic prey-predator system.

Contribution

It provides a comparative analysis showing that common perturbation techniques are ineffective for simple population models.

Findings

Adomian decomposition method fails to model prey-predator dynamics.

Time-series expansion does not accurately describe population interactions.

Homotopy-perturbation and variational-iteration methods also fail.

Abstract

We show that the Adomian decomposition method, the time--series expansion, the homotopy--perturbation method, and the variational--iteration method completely fail to provide a reasonable description of the dynamics of the simplest prey--predator system.