This article is cited in 11 papers

System Analysis and Operations Research

Asymmetric resource networks. II. Flows for large resources and their stabilization

L. Yu. Zhilyakova

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: We study stabilization processes in resource networks with arbitrary topology for large values of the resource, when certain vertices accumulate the resource, and resource in these vertices exceeds output bandwidth. We introduce the notion of flow in a network and study monotone and nonmonotone flows. We prove existence and uniqueness for the limit flow and, as a corollary, of the limit state. We introduce the notion of a potential attractor and study networks with one and several attractors. We show that in networks with several potential attractors, in case of large resources the limit state depends on the initial state.

Presented by the member of Editorial Board: D. A. Novikov

Received: 15.06.2011

 English version: Automation and Remote Control, 2012, 73:6, 1016–1028

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