**:** . .
**:** . II.

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**:**
**:** 2013
**:** ..

** :**
**:** 45
**:** . . . II. / . 45. .: , 2013. .6-29.

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** :** , , , ,

** (.):** diffusion on graphs, resource network, attractors, limit state.

**:** . . , , . , . .

** (.):** We study processes in ergodic nonregular resource networks at high levels of resource. The formula for the threshold value T is derived. It was shown that there are no oscillations if W ? T; the network becomes stable from every initial state when resource level is high. The formulae for the vectors of limit state and the limit flow are derived. The criterion of attractivity of vertices is formulated.

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