具有分布时滞的脉冲种群系统的动力学行为

Dynamics of a Population Model with Impulsive Toxin Input and Distributed Maturation Delay

考虑的是带脉冲毒物输入和时滞的单种群模型的动力学行为,特别地,这里时滞项包含常时滞和分布成熟时滞.通过控制成熟个体的收获率,不仅得到了种群灭绝的充分条件,而且得到了种群灭绝周期解的指数渐近稳定和种群持久性的充分条件.这样的话,通过控制收获率,脉冲周期及脉冲毒物的输入量就能保护物种的数量,从而,结果对生物资源的管理具有一定的意义.

This paper is concerned with the single stage-structured population model with impulsive toxin input and time delays. Furthermore, the mature individuals are harvested continuously and the maturation delay is modelled as a distribution, to allow for the possibility that individuals may take a different time to mature and pollution time delay is a constant. We not only show that the population goes extinct if the harvesting rate is beyond a critical threshold, but also obtain conditions for exponentially asymptotic stability of population-extinction periodic solution and permanence of the population for our model. In this case, we can be easy to control the harvesting rate, the impulsive period and amount of impulsive toxin input to protect the species. Our results contribute to biological resource management.