arXiv 0901.12832009-01-09math.DS

具有分布时滞的方程的绝对稳定性和时滞相关稳定性：从非线性微分方程到差分方程的桥梁

Absolute and Delay-Dependent Stability of Equations with a Distributed Delay: a Bridge from Nonlinear Differential to Difference Equations

Elena Braverman, Sergey Zhukovskiy

备注：: 23 pages, 4 figures

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摘要：

研究了具有正平衡点的分布时滞非线性模型的时滞无关稳定性。这类模型经常出现在种群动力学和其他应用中。特别地，我们构造了一个相关的差分方程，使得它的稳定性意味着具有分布时滞和有限记忆的方程的稳定性。一般来说，这个结果对于具有无限内存的系统是不正确的。如果相关的差分方程是不稳定的，我们描述了一般的时滞无关吸引集，并证明了具有分布时滞的方程是稳定的足够小的延迟。

英文摘要：

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant difference equation such that its stability implies stability of the equation with a distributed delay and a finite memory. This result is, generally speaking, incorrect for systems with infinite memory. If the relevant difference equation is unstable, we describe the general delay-independent attracting set and also demonstrate that the equation with a distributed delay is stable for small enough delays.

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