The effects of impulsive toxicant input on a single-species population in a small polluted environment

Dongmei Li; Tana Guo; Yajing Xu; Dongmei Li; Tana Guo; Yajing Xu

doi:10.3934/mbe.2019413

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 8179-8194. doi: 10.3934/mbe.2019413

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The effects of impulsive toxicant input on a single-species population in a small polluted environment

College of Science, Harbin University of Science Technology, Harbin 150080, China

Received: 31 December 2018 Accepted: 14 May 2019 Published: 10 September 2019

In this paper, we study a single-species population model with pulse toxicant input in a small polluted environment. The intrinsic rate of population change is affected by the environmental toxin load and toxin in the organisms which is influenced by toxin in the environment and the food chain. A new mathematical model is established. By the Pulse Compare Theorem, we find the surviving threshold of the population and obtain the sufficient conditions of persistence and extinction of the population.
- pollution,
- extinction,
- persistence,
- impulsive toxicant input,
- surviving threshold
Citation: Dongmei Li, Tana Guo, Yajing Xu. The effects of impulsive toxicant input on a single-species population in a small polluted environment[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 8179-8194. doi: 10.3934/mbe.2019413

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Abstract

In this paper, we study a single-species population model with pulse toxicant input in a small polluted environment. The intrinsic rate of population change is affected by the environmental toxin load and toxin in the organisms which is influenced by toxin in the environment and the food chain. A new mathematical model is established. By the Pulse Compare Theorem, we find the surviving threshold of the population and obtain the sufficient conditions of persistence and extinction of the population.

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