Maximal total population of species in a diffusive logistic model

Chiu-Yen Kao (Lead / Corresponding author), Seyyed Abbas Mohammadi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we investigate the maximization of the total population of a single species which is governed by a stationary diffusive logistic equation with a fixed amount of resources. For large diffusivity, qualitative properties of the maximizers like symmetry will be addressed. Our results are in line with previous findings which assert that for large diffusion, concentrated resources are favorable for maximizing the total population. Then, an optimality condition for the maximizer is derived based upon rearrangement theory. We develop an efficient numerical algorithm applicable to domains with different geometries in order to compute the maximizer. It is established that the algorithm is convergent. Our numerical simulations give a real insight into the qualitative properties of the maximizer and also lead us to some conjectures about the maximizer.
Original languageEnglish
Article number47
Number of pages27
JournalJournal of Mathematical Biology
Volume85
Issue number5
Early online date7 Oct 2022
DOIs
Publication statusPublished - Nov 2022

Keywords

  • Diffusive logistic equation
  • Optimal control
  • Population dynamics
  • Rearrangements
  • Gradient-based algorithm

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