脉冲作用对环境污染中单种群动力学行为影响

研究了一个在污染环境中的单种群模型,该模型考虑外界污染源在固定时刻排放毒素到本环境中以及在同一时刻考虑通过一些因素作用使该种群生物体排泄毒素.利用脉冲微分方程的比较定理及周期单种群Logistic模型的一些已知结论,证明了当脉冲周期小于某个阈值时,该种群灭绝,反之,则该种群持续生存.并且还证明了上述的持续生存条件也能确保该系统存在惟一的全局渐近稳定的正周期解.

Impact of impulsive effect on a population dynamical behavior in a polluted environment

A mathematical model to study the effect of a toxicant impulsively emitted into the environment from external sources and toxin excreted by some factors on a single biological species, is proposed and analyzed. It is also assumed that the toxicant emission and toxin excretion are used in the same simultaneous periodicity. By using the comparative results of impulsive differential equations and some known results of a single species Logistic model, it is observed that the population is extinct on condition that the impulsive period is lower than some threshold value. When the impulsive period is higher than this critical value, the population is shown to be permanent. It is also proved that the permanent conditions assure that there exists a unique positive periodic solutions which is globally asymptotically stable.