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

  • 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.

    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

    Related Papers:

  • 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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