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** (.):** resource network, graph dynamic threshold model, attractors, capacity limitation

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** (.):** We study the resource redistribution in networks with capacity limitations on so-called attractor-vertices. The stability of the processes for any total amount of resource in such networks is proved. We formulate the criterion of secondary attractivity, and find vectors of limit flow and limit state, formula for the second threshold value of resource II. As indirect results we get several additional characteristics of networks with limitations and without them.

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