DETERMINISTIC AND STOCHASTIC MODELS FOR SPREADING TWO-SPECIES POPULATION

The study of the growth of the interacting populations that spread in the region of space is generally done with the help of either the deterministic equations of reaction-diffusion type or by the stochastic partial differential equations. These stochastic partial differential equations are constructed from the corresponding deterministic evolution equations of reaction diffusion type describing such a population system, by the perturbation of all or some of the parameters of the equations with the white noises. Thus, the deterministic equations are primarily important in the study of an eco-system since they are the basic ingredients for the stochastic model that may be more relevant to the actual situations for the system; apart from their own merit of describing the eco-system in a simpler way. Here, we shall study the equations of both the types for a two-species spreading population with a special kind of interaction among them. But, in the present case we shall begin with the stochastic equations generated from a more general model proposed earlier by the present author (De, 1987; 1991; 1995) and then discuss the corresponding deterministic equations that arise, as the ^byproduct' in the approximate evaluation of the transition probabilities in the stochastic cases. Of course, these equations are themselves relevant for the two-species population because they can describe the deterministic nature of the population growth and pattern.