Perturbations of finite networks and asymptotic periodicity of flow semigroups
The asymptotic behaviour of transport flows in networks and related questions have lately been treated in several articles, extending the original problem from finite to infinite networks and studying several different types of convergence of the corresponding semigroup flow. The goal of this article is a new, less abstract approach to the problem allowing better understanding of the underlying mechanism of flow in networks. The relevance of cycle lengths rather than edge lengths in connection with asymptotic behaviour is examined in Section~3, through a perturbation method applied to the network itself. The perturbation method is presented in the setting of finite strongly connected network. In the author's paper [``Perturbations of networks and asymptotic periodicity of recurrent flows: the infinite case'' (Preprint, 2008)], this technique is adapted to infinite networks, where it allows for significant generalizations of previous results. Also, the author indicates some connections between flows in networks and Markov chains.
scientific article; zbMATH DE number 5614938