A Predator-prey Model with Predator Population Saturation

Abstract

In this article, a new predator-prey model having predator saturation is proposed. The model resembles a classical Rosenzweig-MacArthur type model, but comes with an added function, the population saturation function of the predator. This function of the predator population is a factor in the predator fertility term in the model. Consequently the model behaves better than the Rosenzweig-MacArthur model since all solutions are bounded within the population quadrant. An invariant region arises where the Poincaré-Bendixon theorem can be applied. In most cases there is but a single critical value, either an attracting spiral point suggesting a stable population pair or an unstable node, resulting in a unique limit cycle. This model is fully described and an analysis of the stability of critical values is provided. The robustness of the model is demonstrated based on the classification of Gunawardena [8].

Positive periodic solutions for Lotka–Volterra systems with a general attack rate

“…x = ax 1 − x K − φ(x)y y = −by + cφ(x)y. Some generalizations of the Rosenzweig-MacArthur model are given in [6], where in particular, it is consider the logistic growth for both prey and predator populations (see also [4]).…”