期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 67, 期 5, 页码 1379-1395出版社
SIAM PUBLICATIONS
DOI: 10.1137/060670377
关键词
predator-prey model; stage structure; global stability; uniform persistence; Lya-punov function
The global properties of a predator-prey model with nonlinear functional response and stage structure for the predator are studied using Lyapunov functions and LaSalle's invariance principle. It is found that, under hypotheses which ensure the uniform persistence of the system and the existence of a unique positive steady state, a feasible a priori lower bound condition on the abundance of the prey population ensures the global asymptotic stability of the positive steady state. A condition which leads to the extinction of the predators is indicated. We also obtain results on the existence and stability of periodic solutions. In particular, when (4.2) fails to hold and the unique positive steady state E* becomes unstable, the coexistence of prey and predator populations is ensured for initial populations not on the one-dimensional stable manifold of E*, albeit with fluctuating population sizes.
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