Resource Allocation Among Attractor Vertices in Asymmetric Regular Resource Networks

In this paper, asymmetric regular resource networks with several attractor vertices are considered. It is demonstrated that the resource surplus Δ W = W − T above a threshold value W = T has the same allocation in such a network as in the corresponding absorbing network, which is obtained from the asymmetric one by eliminating the outbound edges of attractors. But there exist corrections depending on the capacities of the outbound edges of attractors and also on the initial resource allocation. Upper bounds of these corrections are derived. The initial states that lead to the exact limit states without any adjustments are determined.