O.V. Druzhinina1, I.I. Vasilyeva2, O.N. Masina3

1 FRС «Computer Science and Control» of Russian Academy of Sciences (Moscow, Russia)
2, 3 Bunin Yelets State University (Yelets, Russia)
1 ovdruzh@mail.ru, 2 irinavsl@yandex.ru, 3olga121@inbox.ru

The study of population dynamics models taking into account competitive interactions and migration flows is of considerable theoretical and applied interest. Important areas are the qualitative analysis of solutions using Lyapunov functions, the identification of features of the trajectory dynamics of multidimensional nonlinear models using numerical methods, as well as the search for parametric sets that ensure the coexistence of species using numerical methods of global optimization. Within the framework of these directions one of the key problems to obtain conditions for the stability of equilibrium states. The objectives of the article are the development of a unified approach to the description of nonlinear dynamic models with migration flows, obtaining conditions for the stability of equilibrium states, and searching for optimal parametric sets. The model "two competitors – two migration areas" is constructed. The Lyapunov function providing the asymptotic stability of the positive equilibrium state is found. The case of pairwise uniform migration is studied. Optimal sets of parameters are obtained based on the differential evolution method. Projections of phase portraits are constructed. The analysis of trajectory dynamics is carried out. The results of computer experiments are presented and the qualitative effects that occur with variable parameters are described. The application of the results is focused on solving the problems of modeling nonlinear dynamic systems. The results can be used to analyze the stability of multidimensional models with migration flows, as well as multidimensional models with symbiotic and trophic interactions.

Druzhinina O.V., Vasilyeva I.I., Masina O.N. Qualitative and numerical study of a four-dimensional dynamic model with competition and migration. Nonlinear World. 2026. V. 24. № 2. P. 14–21. DOI: https:// doi.org/10.18127/ j20700970-202602-02 (In Russian)

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