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Dynamics of solutions of logistic equation with delay and diffusion in a planar domain

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Abstract

We consider a boundary value problem based on a logistic model with delay and diffusion describing the dynamics of changes in the population density in a planar domain. It has spatially inhomogeneous stable solutions branching off from a spatially homogeneous solution and sharing qualitatively the same dynamical properties. We numerically investigate their phase bifurcations with a significant decrease in the diffusion coefficient. The coexisting stable modes with qualitatively different properties are also constructed numerically. Based on the applied numerical and analytic methods, the solutions of the considered boundary value problem are divided into two types, the first of which includes solutions that inherit the properties of the homogeneous solution and the second includes the so-called self-organization modes. Solutions of the second type are more intricately distributed in space and have properties much more preferable from the standpoint of population dynamics.

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Funding

This work was supported by the Russian Science Foundation (grant No. 22-11-00209).

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Authors and Affiliations

  1. Demidov Yaroslavl State University, Yaroslavl, Russia

    V. E. Goryunov

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  1. V. E. Goryunov
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Correspondence to V. E. Goryunov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 212, pp. 234–256 https://doi.org/10.4213/tmf10266.

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Goryunov, V.E. Dynamics of solutions of logistic equation with delay and diffusion in a planar domain. Theor Math Phys 212, 1092–1110 (2022). https://doi.org/10.1134/S0040577922080050

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