Survival analysis of single-species population diffusion models with chemotaxis in polluted environment

Xiangjun Dai; Suli Wang; Baoping Yan; Zhi Mao; Weizhi Xiong; Xiangjun Dai; Suli Wang; Baoping Yan; Zhi Mao; Weizhi Xiong

doi:10.3934/math.2020434

AIMS Mathematics

2020, Volume 5, Issue 6: 6749-6765. doi: 10.3934/math.2020434

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Research article

Survival analysis of single-species population diffusion models with chemotaxis in polluted environment

1.
School of Data Science of Tongren University, Tongren, 554300, PR China
2.
Tongren Preschool Education College, Tongren, 554300, PR China

Received: 14 April 2020 Accepted: 17 August 2020 Published: 01 September 2020
MSC : 92B05, 92D25, 93E03

In this paper, single-species population diffusion models with chemotaxis in polluted environment are proposed and studied. For the deterministic single-species population diffusion model, the sufficient conditions for the extinction and strong persistence of the single-species population are established. For the stochastic single-species population diffusion model. First, we show that system has unique global positive solution. And then, the sufficient conditions for extinction and strongly persistent in the mean of the single-species are obtained. Numerical simulations are used to confirm the efficiency of the main results.
- chemotaxis,
- persistence,
- extinction,
- stochastic perturbations,
- polluted environment
Citation: Xiangjun Dai, Suli Wang, Baoping Yan, Zhi Mao, Weizhi Xiong. Survival analysis of single-species population diffusion models with chemotaxis in polluted environment[J]. AIMS Mathematics, 2020, 5(6): 6749-6765. doi: 10.3934/math.2020434

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Abstract

In this paper, single-species population diffusion models with chemotaxis in polluted environment are proposed and studied. For the deterministic single-species population diffusion model, the sufficient conditions for the extinction and strong persistence of the single-species population are established. For the stochastic single-species population diffusion model. First, we show that system has unique global positive solution. And then, the sufficient conditions for extinction and strongly persistent in the mean of the single-species are obtained. Numerical simulations are used to confirm the efficiency of the main results.

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