The construction and analysis of four-dimensional models of population dynamics taking into account migration flows

The direction associated with the study of multidimensional models of population dynamics is relevant due to the lack of knowledge of nonlinear models of dimension n (n > 3) and in connection with the applied significance for describing ecosystems. The formalized description of a four-dimensional model of population dynamics is proposed, taking into account competition and migration flows. An optimization problem is formulated and solved for finding model parameters that ensure the coexistence of populations under conditions of competition between two species in the main area, taking into account the migration of these species. Considered within the framework of the optimization problem, the quality criterion ensures the fulfillment of the conditions for the coexistence of populations. In order to solve the optimization problem, an evolutionary search algorithm is developed. For the proposed population-migration model, the qualitative behavior is studied, projections of phase portraits are constructed, trajectories are found for different sets of model parameters. The comparative analysis of the results of numerical experiments on the search for model trajectories is given. Computational experiments are performed using the developed software package. The obtained results can be used in modeling ecological, socio-economic, demographic and physico-chemical processes.