带有阶段结构的时滞捕食-被捕食动力系统的全局稳定性和最优收获量

讨论捕食和被捕食动力系统时，把生物种群分为幼年和成年两个阶段，仅成年有捕食能力。还考虑了种群相互作用中不可避免的时滞和密度制约作用，以及在捕食一被捕食模型中更切合实际的“比率依赖”理论。通过对系统的分析和构造李雅普诺夫函数，分别得出在适当条件下系统非负平衡位置的局部稳定性和全局稳定性。并研究了成熟种群的最优收获量。

Stability and Optimal Harvesting of a Delayed Ratio-Dependent Predator-Prey System with Stage Structure

A stage-structured predator-prey system of population growth con-sisting of immature and mature individuals is proposed with a mature population ofharvesting, the growth of predator population is of Holling Ⅱ type with time delay andratio-dependent(which can be roughly stated as that the per capita predator growthrate should be a function of the ratio of prey to predator abundance). We establishconditions under which positive equilibrium of the system is locally and globally asymp-totically stable and the optimal harvesting of the mature population is also considered.