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.
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Werner Krabs (2003) studied this question.
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