污染环境中时滞对种群的影响

Effects of Time Delay on a Population in a Polluted Environment

有害的化学物质浸入到环境后，造成了环境污染，暴露在此环境中的生物种群，其持续生存性受到威胁。在生态毒理学中研究种群的风险估计具有重要的现实意义。生态数学家Ｈａｌｌａｍ，Ｔ，Ｇ．教授等在１９８３年首先建立了污染环境条件下生物种学的动力学模型（Ｈａｌｌａｍ，１９８３）；马知恩教授和Ｈａｌｌａｍ教授提出了积分平均的方法，用此方法他们得到了生物种群生存和绝灭的条件，并且在一定条件下得到了生存与绝灭的充分必要条件－阈值（马知恩，１９８６）；马知恩，宋保军和Ｈａｌｌａｍ合作，同样用积分均值的方法得到了一般条件下生物种群持续生存和绝灭的阈值（马知恩，１９８９）。本文中，建立了毒素和生物种群具有时滞作用时种群的动力学模型，该模型比以往的模型更加符合实际，通过对所建数学模型的研究，同样得到了生物种群持续生存和绝灭的阈值，该阈值表明，毒素时滞的作用会使种群更容易灭绝，而种群自身的时滞作用对该阈值无影响。

Abstract In this article,a population dynamic model with time delay on both population and toxicant has been established. This model is more practical than those models which have been considered before. A threshold between persistence and extinction of the population has also been obtained for our model. This threshold shows that the population is easier to go to extinction if toxicant is affected by delay,and that there is no effect on the threshold even if the population is affected by delay.