摘要
研究一个具有时滞和捕食者、食饵均具有阶段结构的捕食者-食饵模型的稳定性.通过分析特征方程,运用Hurwitz判断定理,讨论了该模型非负平衡点的局部稳定性,并得到了Hopf支存在的充分条件;通过构造适当的Lyapunov泛函,运用LaSalle不变集原理,讨论了该模型的非负平衡点的全局稳定性,从而得到了保证该生态系统永久持续生存与灭绝的充分条件.
The stability of a predator-prey model with time delay and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each feasible equilibria of the system is discussed and the existence of a Hopf bifurcation at the positive equilibrium is established. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each feasible equilibria of the model is discussed.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2013年第4期466-476,共11页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(11101117)
