Abstract:
We study nonsymmetric regular resource networks with several attractor-vertices. In these networks there exists a threshold value of total resource $W = T$, such that for any initial distribution the limit state is uniquely determined, but when $W > T$ extra resource $\Delta W = W-T$ allocates among attractor-vertices depending on the initial state. We prove that this allocation obeys the same law as the allocation in corresponding absorbing network (derived from asymmetric by deletion output edges of attractors). However, there are adjustments dependent on the graph characteristics and the initial distribution of resources. The upper bounds of these adjustments are estimated. The initial states are determined that lead to precise limit states with no adjustments.
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