Algorithm for studying the dynamics of a spatially distributed logistic equation with delay and taking into account migration
https://doi.org/10.18255/1818-1015-2025-3-242-251
Abstract
The logistic equation with delay and diffusion, which is important in mathematical ecology, is considered. It is assumed that the boundary conditions at one end of the interval [0,1] contain a parameter. The question of local — in the neighborhood of the equilibrium state — dynamics of the corresponding boundary value problem for all values of the boundary condition parameters is investigated. Critical cases in the problem of stability of the equilibrium state are identified and normal forms — scalar complex ordinary differential equations of the first order — are constructed. Their nonlocal dynamics determine the behavior of solutions of the original problem in a small neighborhood of the equilibrium state.
Supporting agencies: This work was carried out within the framework of a development programme for the Regional Scientific and Educational Mathematical Center of the Yaroslavl State University with financial support from the Ministry of Science and Higher Education of the Russian Federation (Agreement on provision of subsidy from the federal budget No. 075-02-2025-1636)
About the Authors
Dmitry S. Kashchenko
P.G. Demidov Yaroslavl State University
Russian Federation
Russian Federation
Dmitry O. Loginov
P.G. Demidov Yaroslavl State University
Russian Federation
Russian Federation
Anna O. Tolbey
P.G. Demidov Yaroslavl State University
Russian Federation
Russian Federation
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Review
For citations:
Kashchenko D.S., Loginov D.O., Tolbey A.O. Algorithm for studying the dynamics of a spatially distributed logistic equation with delay and taking into account migration. Modeling and Analysis of Information Systems. 2025;32(3):242-251. (In Russ.) https://doi.org/10.18255/1818-1015-2025-3-242-251
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