UNIFORM PERSISTENCE IN FUNCTIONAL-DIFFERENTIAL EQUATIONS
UNIFORM PERSISTENCE IN FUNCTIONAL-DIFFERENTIAL EQUATIONS
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DOI：
10.1006/jdeq.1995.1011
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发表时间：
1995-01-01
影响因子：
2.4
通讯作者：
RUAN, SG
中科院分区：
文献类型：
--
作者：
FREEDMAN, HI;RUAN, SG
本文研究了时滞泛函微分方程的一致持久性问题。通过利用Liapunov函数，Razumikhin技术和微分不等式，我们能够建立一致持久性的标准，类似于其他常微分方程，差分方程和反应扩散方程。我们将这些准则应用到一些著名的生物时滞模型。我们的结果表明，保证内部平衡点存在的条件足以保证一致持久性。此外，这些条件也等价于无时滞情形的一致持久性。(C)1995学术出版社，Inc.
In this paper, we investigate the question of uniform persistence for retarded functional differential equations. By utilizing Liapunov-like functions, Razumikhin techniques, and differential inequalities, we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations, difference equations, and reaction-diffusion equations. We apply these criteria to some well known biological models with delay. Our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence. Moreover, these conditions are equivalent to uniform persistence for the cases without delay as well. (C) 1995 academic Press, Inc.