A.A. Davydov, D.A. Melnik. Optimal states of distributed exploited populations with periodic impulse selection ... P. 99-107

The dynamics of a population distributed on a torus is described by an equation of the Kolmogorov–Petrovsky–Piskunov–Fisher type in the divergence form. The population is exploited by periodic sampling of a constant distributed measurable ratio of its density. We prove that there exists a sampling ratio maximizing the time-averaged income in kind, i.e., a ratio that provides an optimal stationary exploitation in the long run.

Keywords: distributed population, Kolmogorov–Petrovsky–Piskunov–Fisher equation, impulse control, optimal solution

Received March 30, 2021

Revised April 12, 2021

Accepted April 19, 2021

Funding Agency: This work was supported by the Ministry of Science and Higher Education of the Russian Federation (the first author, results on the properties of the quality functional, project no. 0718-2020-0025) and by the Russian Science Foundation (both authors, main theorem, project no. 19-11-00223).

Alexey Alexandrovich Davydov, Dr. Phys.-Math. Sci., Prof., Lomonosov Moscow State University, Moscow, 119992 Russia; National University of Science and Technology MISIS, Moscow, 119049 Russia, e-mail: davydov@mi-ras.ru

Dzhamilia Arturovna Melnik, undergraduate student, Lomonosov Moscow State University, Moscow, 119992 Russia. e-mail: dzhamilya.saidzhanova@gmail.com

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Cite this article as: A.A. Davydov, D.A. Melnik. Optimal states of distributed exploited populations with periodic impulse selection, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 2, pp. 99–107; Proceedings of the Steklov Institute of Mathematics (Suppl.), 2021, Vol. 315, Suppl. 1, pp. S81–S88.