Stability in predator - prey models and discretization of a modified Volterra - Lotka model

We consider n ⩾ 2 populations of animals 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 derive sufficient conditions for this equilibrium state to be stable by Lyapunov's method. The results supplement those published elsewhere. Further we consider a modification of the Volterra - Lotka model which admits an asymptotically stable steady state solution. This model is discretized in two ways and we investigate how small the time step size has to be chosen in order to guarantee that the steady state solution is an attractive fixed point of the discretized model. This investigation is connected with the determination of the model parameters from given data.