Asymmetric resource networks. III. A study of limit states

This work is devoted to methods of computing the limit state and the limit flow in a resource network for large values of the resource. To do so, we study resource distribution processes in families of networks with various bandwidth matrices corresponding to the same stochastic matrix. The threshold value of the resource $T$ such that the network operates differently on both sides of this value and the coordinates of the limit state vector for vertices that are not attractors are expressed via parameters of the bandwidth matrix and the limit transitions matrix for the Markov chain corresponding to the stochastic matrix in question. If the network has several potential attractors, the limit amount of resource in them depends on the initial state.