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We discuss a model of motion of substance through the nodes of a channel of a network. The channel can be modeled by a chain of urns where each urn can exchange substance with the neighboring urns. In addition the urns can exchange substance with the network nodes and the new point is that we include in the model the possibility for exchange of substance among the urns (nodes) and the environment of the network. We consider stationary regime of motion of substance through a finite channel (stationary regime of exchange of substance along the chain of urns) and obtain a class of statistical distributions of substance in the nodes of the channel. Our attention is focused on this class of distributions and we show that for the case of finite channel the obtained class of distributions contains as particular cases truncat
Many systems such as critical infrastructure exhibit a modular structure with many links within the modules and few links between them. One approach to increase the robustness of these systems is to reinforce a fraction of the nodes in each module, s
Intervals between discrete events representing human activities, as well as other types of events, often obey heavy-tailed distributions, and their impacts on collective dynamics on networks such as contagion processes have been intensively studied.
Cycles, which can be found in many different kinds of networks, make the problems more intractable, especially when dealing with dynamical processes on networks. On the contrary, tree networks in which no cycle exists, are simplifications and usually
In this paper we show that the small world and weak ties phenomena can spontaneously emerge in a social network of interacting agents. This dynamics is simulated in the framework of a simplified model of opinion diffusion in an evolving social networ
We discuss a channel consisting of nodes of a network and lines which connect these nodes and form ways for motion of a substance through the channel. We study stationary flow of substance for channel which arms contain finite number of nodes each an