Majewsky O. Modelling predator - prey natural systems in their polluted inhabitable environment

Research aimed at solving scientific and applied problems of increase of efficiency of process modeling the dynamics of the natural systems of the type "predator - prey" through the development of mathematical models with given initial conditions on the spatial-temporal modelling. Object of research are the processes of modeling dynamics in natural systems of the type "predator - prey". Used methods of system analysis, mathematical modeling, methods, set theory, statistical processing of information, methods of computational mathematics, programming. Theoretical value - the proposed new mathematical model of interaction between predator - prey" as taking into account the effect of diffusion, and without it (by using a generalized model of system evolution). The scientific novelty of the obtained results: the expediency of application of the generalized model of evolution of natural systems to study the processes of population dynamics of predators and prey in natural interaction systems "predator - prey" taking into account the influence of the external environment; development of a mathematical interaction model "predator - prey", which differs from the known presence of components that take into account the influence of the external environment, which allows to adequately simulate dynamics in natural systems; developed a mathematical model of the dynamics of interacting natural systems "predator - prey" taking into account the effect of diffusion, which differs from known factors to influence the environment of their existence that provides the ability to predict the distribution of predators and prey in a particular area. Practical implications: the proposed model adequately reproduce the population dynamics of the predator and its prey in ecosystems and their distribution in the study area with an acceptable error.