The optimal distribution of resources and rate of migration maximizing the population size in logistic model with identical migration

Xing Liang; Lei Zhang

doi:10.3934/dcdsb.2020280

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2021, Volume 26, Issue 4: 2055-2065. Doi: 10.3934/dcdsb.2020280

This issue Previous Article Asymptotic dynamics of hermitian Riccati difference equations Next Article On the semilinear fractional elliptic equations with singular weight functions

The optimal distribution of resources and rate of migration maximizing the population size in logistic model with identical migration

Xing Liang^1, , and
Lei Zhang^2,

1.
School of Mathematical Sciences and Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
2.
Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong 264209, China

^* Corresponding author: Xing Liang
^* Corresponding author: Xing Liang

Dedicated to Professor Sze-Bi Hsu on the occasion of his 70th birthday

Received: April 30, 2020

Revised: July 31, 2020

Early access: September 2020

Published: April 2021

Liang's research is supported by the National Natural Science Foundation of China (11971454) and the Fundamental Research Funds for the Central Universities; Zhang's research is supported by the National Natural Science Foundation of China(11901138) and Natural Science Foundation of Shandong Province (ZR2019QA006)

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Abstract

This paper focuses on an optimization problem arising in population biology. We investigate the effect of the resources distribution and the migration rate on the total population size of some species, which migrates among patches with the identical probability and grows logistically in each patch. We aim to maximize the total population size by the distribution of resources and the rate of migration.

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Mathematics Subject Classification: Primary: 92B05; Secondary: 92D40.

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