This article is cited in 3 papers

Communication Network Theory

Global Stability of Infinite Systems of Nonlinear Differential Equations and Nonhomogeneous Countable Markov Chains

V. I. Oseledets, D. V. Khmelev


Abstract: Countable systems of differential equations $\dot x=f(x)$ in $X\subset l_1$ with bounded Jacobi operators $J(x)=\partial f/\partial x$ are studied. Sufficient conditions of global stability and global asymptotic stability are obtained, where for any $x\in X$ the matrix $J^T(x)$ is the transition-rate matrix for a countable Markov chain and $X$ is a subset of a linear affine variety. Results are applied to two infinite systems arising from the modern queueing theory.

UDC: 621.391.1:519.27

Received: 30.04.1999

 English version: Problems of Information Transmission, 2000, 36:1, 54–70

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