A solution to the accelerated-predator-satiety Lotka–Volterra predator–prey problem using Boubaker polynomial expansion scheme

Abstract

In this study, an analytical method is introduced for the identification of predator–prey populations time-dependent evolution in a Lotka–Volterra predator–prey model which takes into account the concept of accelerated-predator-satiety.

Oppositely to most of the predator–prey problem models, the actual model does not suppose that the predation is strictly proportional to the prey density. In reference to some recent experimental results and particularly to the conclusions of May (1973) about predators which are ‘never not hungry’, an accelerated satiety function is matched with the initial conventional equations. Solutions are plotted and compared to some relevant ones. The obtained trends are in good agreement with many standard Lotka–Volterra solutions except for the asymptotic behaviour.