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Discrete-time model for a motion of substance in a channel of a network with application to channels of human migration

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Vitanov,  Nikolay K.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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https://www.sciencedirect.com/science/article/pii/S037843711830801X
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1807.08778.pdf
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Citation

Vitanov, N. K., & Vitanov, K. N. (2018). Discrete-time model for a motion of substance in a channel of a network with application to channels of human migration. Physica A, 509, 635-650. doi:10.1016/j.physa.2018.06.076.


Cite as: https://hdl.handle.net/21.11116/0000-0002-5BBE-3
Abstract
We discuss a discrete-time model for motion of substance in a channel of a network. For the case of stationary motion of the substance and for the case of time-independent values of the parameters of the model we obtain a new class of statistical distributions that describe the distribution of the substance along the nodes of the channel. The case of interaction between a kind of substance specific for a node of the network and another kind of substance that is leaked from the channel is studied in presence of possibility for conversion between the two substances. Several scenarios connected to the dynamics of the two kinds of substances are described. The studied models: (i) model of motion of substance through a channel of a network, and (ii) model of interaction between two kinds of substances in a network node connected to the channel, are discussed from the point of view of human migration dynamics and interaction between the population of migrants and the native population of a country. (C) 2018 Elsevier B.V. All rights reserved.