Mathematical Model of Ideal Free Distribution in the Predator–Prey System

We consider a system of reaction-diffusion-advection equations that describes the evolution of spatial distributions of antagonistic populations under directed migration. The concept of an ideal free distribution (IFD) for a predator-prey system is introduced. We find conditions on parameters under...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.285 (3), p.328-338
Main Authors: Zelenchuk, P. A., Tsybulin, V. G.
Format: Article
Language:English
Subjects:
Advection-diffusion equation
Asymptotic series
Dimensional analysis
Mathematics
Mathematics and Statistics
Predators
Spatial distribution
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Summary:We consider a system of reaction-diffusion-advection equations that describes the evolution of spatial distributions of antagonistic populations under directed migration. The concept of an ideal free distribution (IFD) for a predator-prey system is introduced. We find conditions on parameters under which there exist explicit stationary solutions with nonzero densities of both species. The numerical approach with staggered grids is used to analyze solutions in case of violation of the conditions on the coefficients that provide the IFD. We construct asymptotic expansions for an inhomogeneous one-dimensional area and present the results of a computational experiment in the case of violation of the IFD conditions.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07445-x