I.I. Vasilyeva1

1 Bunin Yelets State University (Yelets, Russia)
1 irinavsl@yandex.ru

Multidimensional migration-population models with predator–prey interactions are an important class of nonlinear dynamic models. The work is devoted to the construction and analysis of five–dimensional dynamic population models related to the type "two prey – one migration area – predator – super predator". The essential aspects of studying such models are the search for parameters that ensure the coexistence of species, the analysis of stationary modes, the determination of the nature of trajectories, as well as the transition to stochastic cases that take into account the influence of additive and multiplicative noise on the dynamics of the model. The aim of the work is construction, qualitatively analyze and stochastization a five-dimensional population model with migration flows taking into account trophic interactions, clarification the influence of additive and multiplicative noise on the system dynamics. Deterministic and stochastic models "two prey – one migration area – predator – super predator" are constructed. The modeling of the processes of species interaction in conditions of trophic interactions and migration flows is carried out. A series of computer experiments are performed, projections of phase portraits are constructed, qualitative effects are identified and a transition to the stochastic case is made, taking into account the addition of additive and multiplicative noise to the right-hand sides of the equations of the system. Trajectory dynamics is studied for stochastic models. The results can be used in solving problems of analyzing complex dynamic systems taking into account random factors.

Vasilyeva I.I. A study of stochastic migration and population models “two prey – one migration area – predator – super predator”. Nonlinear World. 2025. V. 23. № 2. P. 5–14. DOI: https:// doi.org/10.18127/ j20700970-202501-01 (In Russian)

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