Some industrial behaviors, such as wasting outputs and inadequately treated and stored hazardous materials, may pollute our environment, so some populations in the polluted habitats are at the edge of extinction. In this work, we develop a mathematical model that validates the dynamics of the food-chain population in a polluted environment with impulsive toxicant input. Based on the model, we obtain a sufficient condition for the extinction of populations. When the concentration of toxicants surpasses the threshold, it will contribute to the extinction of populations in the related environment. Also, sufficient conditions for the permanence of populations are obtained in our analysis. Several numerical simulations validate the theoretical conclusions and further reflect the influence of toxicants.

中文翻译：

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脉冲输入毒物的污染环境中食物链种群的动态

一些工业行为，例如浪费产出以及未充分处理和存储有害物质，可能会污染我们的环境，因此受污染的栖息地中的某些人口处于灭绝的边缘。在这项工作中，我们开发了一个数学模型，该模型可以验证在具有脉冲毒物输入的污染环境中食物链种群的动态。基于该模型，我们获得了灭绝种群的充分条件。当有毒物质的浓度超过阈值时，将导致相关环境中种群的灭绝。同样，在我们的分析中也获得了足够的人口永久性条件。若干数值模拟验证了理论结论，并进一步反映了有毒物质的影响。