On Some Perturbation Approaches to Population Dynamics

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. In is well known that a reasonable description of the dynamics of a nonlinear system by means of a perturbation method is a difficult enterprize [1]. Recently, several approaches have been proposed for the treatment of the simplest model for the prey–predator interaction. They are based on the Adomian descomposition method [2], the time–series expansion [3], the homotopy–perturbation method [4, 5], and the variational–iteration method [6]. We have already shown that the time–power series given by the implementation of the homotopy–perturbation method proposed by Chowdhury et al [5] completely fails to yield the main features of the population dynamics [7]. In this short communication we briefly analyze the results of the other proposals in terms of what one expects from an approach designed to solve problems of population dynamics [1]. ∗e–mail: [email protected]