具有Holling Ⅲ功能反应和阶段结构的Gompertz生态系统的持久性

Permanence of a Gompertz Ecosystem with Holling Ⅲ Functional Response and Stage Structure for Predator

以生态学与微分方程的理论和方法为基础,建立了一类具有HollingⅢ功能反应和阶段结构的生态Gompertz模型.利用频闪映射,获得了捕食者灭绝周期解,分析了此周期解的全局吸引性.在对食饵进行脉冲收获和捕食者具有成长期时滞条件下,运用脉冲微分方程比较定理和小振幅扰动技巧,获得了系统一致持续生存的条件.

In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological Gompertz model with Holling Ⅲ functional response and stage structure for predator is established.By use of the stroboscopic map,a predator extinction periodic solution is obtained,and the global attractivity of the predator extinction periodic solution is analyzed.By using comparison theorem of impulsive differential equation and small amplitude perturbation skills,we get the sufficient condition for permanence of the system under impulsive harvest strategy for the prey and maturation time delay of predator.