Uncertainty Treatment in Prey-Predator Models Using Differential Inclusions

The prey-predator model in the form of Lotka-Volterra equation represents a nonlinear description of the dynamics of two or more interacting populations. In this article, several versions of the Lotka-Volterra model are analyzed from the point of view of parameter uncertainty. The uncertainty treatment is quite different from the common approach. We do not treat uncertain parameters as random. Instead, we analyze the behavior of the models supposing that the uncertain parameters may change in time within given limits. The simulation tool used in this paper is based on the differential inclusions, instead of the ordinary differential equations. This permits us to determine the attainable sets in the state space, due to the parameter uncertainty.