Effects of impulsive harvesting and an evolving domain in a diffusive logistic model*

Yue Meng, Zhigui Lin*, Michael Pedersen

*Corresponding author for this work

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Abstract

In order to understand how the combination of the evolution of a domain and impulsive harvesting affect the dynamics of a population, we investigate a diffusive logistic population model with impulsive harvesting on a periodically evolving domain. Initially the ecological reproduction index of the impulsive problem is introduced and given by an explicit formula, which depends on the
domain evolution rate and the impulsive function. Then the threshold dynamics of the population subject to monotone or nonmonotone impulsive harvesting are established based on this index. Finally numerical simulations are carried out to illustrate our theoretical results, and these reveal that a large domain evolution rate can improve the populations ability to survive, no matter which impulsive harvesting takes place. On the contrary, impulsive harvesting has a negative effect on the survival of the population, and can even lead to its extinction.
Original languageEnglish
JournalNonlinearity
Volume34
Issue number10
Pages (from-to)7005–7029
ISSN0951-7715
DOIs
Publication statusPublished - 7 Sep 2021

Keywords

  • Impulsive harvesting
  • Evolving domain
  • Ecological reproduction index
  • Threshold dynamics
  • Persistence and extinction

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