Dynamics of a toxin-mediated aquatic population model with delayed toxic responses

Yueping Dong; Jianlu Ren; Qihua Huang; Yueping Dong; Jianlu Ren; Qihua Huang

doi:10.3934/mbe.2020315

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5907-5924. doi: 10.3934/mbe.2020315

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Dynamics of a toxin-mediated aquatic population model with delayed toxic responses

1.
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
2.
School of Mathematical and Statistical Sciences, Southwest University, Chongqing 400715, China

Received: 30 June 2020 Accepted: 20 August 2020 Published: 04 September 2020

Traditional mathematical models for studying the effects of environmental toxins on population dynamics usually assume that the toxic effects are immediate. However, the effects of toxins on the reproduction and mortality of aquatic populations can be delayed in reality. In this paper, we propose a new mathematical model with delayed toxic responses for aquatic populations in polluted aquatic environments. The delayed model is analyzed in terms of steady states, stability, and bifurcation. The results show that the delayed effect on the reproduction of aquatic populations does not affect the stability of the interior equilibrium, but the delayed effect on the mortality of aquatic populations can destabilize the interior equilibrium. Numerical results corroborate the theoretical ones are presented.
- aquatic population model,
- toxin,
- time delays,
- stability and bifurcation analysis
Citation: Yueping Dong, Jianlu Ren, Qihua Huang. Dynamics of a toxin-mediated aquatic population model with delayed toxic responses[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5907-5924. doi: 10.3934/mbe.2020315

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Abstract

Traditional mathematical models for studying the effects of environmental toxins on population dynamics usually assume that the toxic effects are immediate. However, the effects of toxins on the reproduction and mortality of aquatic populations can be delayed in reality. In this paper, we propose a new mathematical model with delayed toxic responses for aquatic populations in polluted aquatic environments. The delayed model is analyzed in terms of steady states, stability, and bifurcation. The results show that the delayed effect on the reproduction of aquatic populations does not affect the stability of the interior equilibrium, but the delayed effect on the mortality of aquatic populations can destabilize the interior equilibrium. Numerical results corroborate the theoretical ones are presented.

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