Global Dynamics of a Predator-prey Model with Stage Structure for Predator

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题名:	Global Dynamics of a Predator-prey Model with Stage Structure for Predator
作者:	(Paul Georgescu);謝英恒*
贡献者:	公共衛生學院公共衛生學系
日期:	2007-10
上传时间:	2009-08-25 13:32:57 (UTC+8)
摘要:	Abstract. 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.
關聯:	SIAM JOURNAL ON APPLIED MATHEMATICS (67 )1379 ~1395
显示于类别:	[公共衛生學系暨碩博班] 期刊論文

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