Construction and analysis of nondeterministic models of population dynamics

Abstract

Three-dimensional mathematical models of population dynamics are considered in the paper. Qualitative analysis is performed for the model which takes into account the competition and diffusion of species and for the model which takes into account mutual interaction between the species. Nondeterministic models are constructed by means of transition from ordinary differential equations to differential inclusions, fuzzy and stochastic differential equations. Using the principle of reduction, which allows us to study stability properties of one type of equations, using stability properties of other types of equations, as a basis, sufficient conditions of stability are obtained. The synthesis of the corresponding stochastic models on the basis of application of the method of construction of stochastic self-consistent models is performed. The structure of these stochastic models is described and computer modelling is carried out. The obtained results are aimed at the development of methods of analysis of nondeterministic nonlinear models.