**:** . .
**:** . I.

**:** 43
**:**
**:** 2013
**:** . . . I. / . 43. .: , 2013. .34-54.

** :** , , , ,

** (.):** resource network, stochastic matrix, ergodic Markov chain, equilibrium, limit state

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

** (.):** We study operation of ergodic nonregular resource networks when total amount of resource is small. We show that for an arbitrary initial state undamped oscillations occur between several limit vectors. The number of different limit vectors is equal to the number of cyclic classes of a network. The global equilibrium can be achieved when all limit vectors coincide. We derive conditions on initial states leading to the global equilibrium, and obtain formulae for the limit powers of stochastic matrices and for limit vectors.

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