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.

中文翻译：

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具有毒性反应延迟的毒素介导的水生种群模型的动力学

用于研究环境毒素对种群动态影响的传统数学模型通常假定毒性作用是即时的。然而，实际上，毒素对水生种群繁殖和死亡的影响可以被延迟。在本文中，我们提出了一种对污染水生环境中的水生种群具有延迟毒性反应的新数学模型。根据稳态，稳定性和分叉来分析延迟模型。结果表明，对水生种​​群繁殖的延迟影响不影响内部平衡的稳定性，但对水生种群死亡率的延迟影响可破坏内部平衡的稳定性。数值结果证实了理论值。