In this work, we consider a single population-hibernation model with genic mutation, birth pulse and impulsive input toxin in a polluted environment. By the theories of discrete dynamical system and the methods of mathematical analysis, the population-extinction periodic solution \((0,0,c_{o}(t),c_{e}(t))\) of system (2.1) is proved to be globally asymptotically stable. System (2.1) is proved to be permanent. Our results indicate that the genic mutational rate and the amount of the impulsive inputting toxin play important roles on the permanence of system (2.1). Our results also provide reliable tactics for biological resource management.

中文翻译：

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污染环境中具有基因突变和冲动效应的种群冬眠模型的动力学

在这项工作中，我们考虑了在污染环境中具有基因突变、出生脉冲和脉冲输入毒素的单一种群冬眠模型。根据离散动力系统理论和数学分析方法，系统(2.1)的种群灭绝周期解\((0,0,c_{o}(t),c_{e}(t))\ )被证明是全局渐近稳定的。系统（2.1）被证明是永久的。我们的结果表明基因突变率和冲动输入毒素的数量对系统（2.1）的持久性起着重要作用。我们的结果还为生物资源管理提供了可靠的策略。