Single-species population models with stage structure and partial tolerance in polluted environments

Xingmin Wu; Fengying Wei; Xingmin Wu; Fengying Wei

doi:10.3934/mbe.2022446

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 9: 9590-9611. doi: 10.3934/mbe.2022446

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Single-species population models with stage structure and partial tolerance in polluted environments

Xingmin Wu ^{1
,
,},
Fengying Wei ^{1,2
,
,}

1.
School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, China
2.
Key Laboratory of Operations Research and Control of Universities in Fujian, Fuzhou University, Fuzhou 350116, China

Academic Editor: Sanling Yuan

Received: 01 May 2022 Revised: 23 May 2022 Accepted: 31 May 2022 Published: 01 July 2022

We propose stage-structured single-species population models with psychological effects and partial tolerance in polluted environments in this paper. First, the conditions of extinction and the time for extinction are investigated respectively. Especially, the time for extinction takes longer as the value of the psychological effects increases. Then the weak persistence in the mean around the pollution-free equilibrium and the stochastic permanence have been derived under some moderate conditions. Further, the existence of a periodic solution for the periodic single-species population has been determined. The corresponding numerical simulations verify the efficiency of the main theoretical results.
- single-species population model,
- stage-structured,
- psychological effects,
- periodic solution,
- survival level
Citation: Xingmin Wu, Fengying Wei. Single-species population models with stage structure and partial tolerance in polluted environments[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 9590-9611. doi: 10.3934/mbe.2022446

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Abstract

We propose stage-structured single-species population models with psychological effects and partial tolerance in polluted environments in this paper. First, the conditions of extinction and the time for extinction are investigated respectively. Especially, the time for extinction takes longer as the value of the psychological effects increases. Then the weak persistence in the mean around the pollution-free equilibrium and the stochastic permanence have been derived under some moderate conditions. Further, the existence of a periodic solution for the periodic single-species population has been determined. The corresponding numerical simulations verify the efficiency of the main theoretical results.

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