Portal de Periódicos da CAPES

A General Predator-Prey Model

2003; Taylor & Francis; Volume: 9; Issue: 4 Linguagem: Inglês

10.1076/mcmd.9.4.387.27896

1744-5051

Werner Krabs,

Mathematical and Theoretical Epidemiology and Ecology Models

We consider n = 2 populations of animals or plants that are living in mutual predator-prey relations or are pairwise neutral to each other. We assume the temporal development of the population densities to be described by a system of differential equations which has an equilibrium state solution. We at first give sufficient conditions for this equilibrium state to be asymptotically stable by linearizing the system around it. Then we derive sufficient conditions for asymptotic stability by Lyapunov’s method. Finally we investigate a discretization of the Volterra-Lotka model.