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

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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.

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Authors and Affiliations

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

    L. Yu. Zhilyakova

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  1. L. Yu. Zhilyakova
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Original Russian Text © L.Yu. Zhilyakova, 2012, published in Avtomatika i Telemekhanika, 2012, No. 6, pp. 103–118.

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Zhilyakova, L.Y. Asymmetric resource networks. II. Flows for large resources and their stabilization. Autom Remote Control 73, 1016–1028 (2012). https://doi.org/10.1134/S0005117912060070

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  • DOI: https://doi.org/10.1134/S0005117912060070

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