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The optimal distribution of resources and rate of migration maximizing the population size in logistic model with identical migration. (English) Zbl 1466.92150

Summary: 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.

MSC:

92D25 Population dynamics (general)
92D40 Ecology
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[1] L. J. S. Allen; B. M. Bolker; Y. Lou; A. L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic patch model, SIAM J. Appl. Math., 67, 1283-1309 (2007) · Zbl 1121.92054 · doi:10.1137/060672522
[2] X. Bai; X. He; F. Li, An optimization problem and its application in population dynamics, Proc. Amer. Math. Soc., 144, 2161-2170 (2016) · Zbl 1381.35185 · doi:10.1090/proc/12873
[3] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994. · Zbl 0815.15016
[4] R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Wiley, Chichester, 2004. · Zbl 1059.92051
[5] W. Ding; H. Finotti; S. Lenhart; Y. Lou; Q. Ye, Optimal control of growth coefficient on a steady-state population model, Nonlinear Anal. Real World Appl., 11, 688-704 (2010) · Zbl 1182.49036 · doi:10.1016/j.nonrwa.2009.01.015
[6] F. G. Frobenius, Über matrizen aus nicht negativen elementen, S.-B. Deutsch. Akad. Wiss. Berlin, v. 1912,456-477. · JFM 43.0204.09
[7] Y. Lou, On the effects of migration and spatial heterogeneity on single and multiple species, J. Differential Equations, 223, 400-426 (2006) · Zbl 1097.35079 · doi:10.1016/j.jde.2005.05.010
[8] Y. Lou, Some reaction diffusion models in spatial ecology, Sci. Sin. Math., 45, 1619-1634 (2015) · Zbl 1499.35346 · doi:10.1360/N012015-00233
[9] I. Mazari; G. Nadin; Y. Privat, Optimal location of resources maximizing the total population size in logistic models, J. Math. Pure. Appl., 134, 1-35 (2020) · Zbl 1433.92038 · doi:10.1016/j.matpur.2019.10.008
[10] K. Nagahara and E. Yanagida, Maximization of the total population in a reaction-diffusion model with logistic growth, Calc. Var. Partial Differential Equations, 57, (2018), Paper No. 80, 14 pp. · Zbl 1398.35091
[11] O. Perron, Zur theorie der matrices, Math. Ann., 64, 248-263 (1907) · JFM 38.0202.01 · doi:10.1007/BF01449896
[12] H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, 41, American Mathematical Society, Providence, 2008.
[13] X.-Q. Zhao, Dynamical Systems in Population Biology, \(2^{nd}\) edition, Springer, New York, 2017.
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