Geodesic
The problem of finding the initial state of a resource network
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Tome 209 (2022), pp. 42-52

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In this paper, we study distributions of resource flows in resource networks. The main problem is to develop methods for finding the initial state (distribution) of resources in a resource network if the state is known at some moment of discrete time. An essential feature is the significant nonlinearity of the resource redistribution process in such networks. We prove that the problem of finding the initial state is solvable and propose approaches for refining the solution and finding the initial state of the resource network in the cases of large and small resources.
Keywords: dynamic network, ergodic resource network, resource flow, flow distribution, threshold value, initial state of the resource network. 
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     author = {V. A. Skorokhodov and I. M. Erusalimskyi and S. Ch. Murtuzalieva},
     title = {The problem of finding the initial state of a resource network},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {42--52},
     publisher = {mathdoc},
     volume = {209},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_209_a4/}
}
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V. A. Skorokhodov; I. M. Erusalimskyi; S. Ch. Murtuzalieva. The problem of finding the initial state of a resource network. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Tome 209 (2022), pp. 42-52. http://geodesic.mathdoc.fr/item/INTO_2022_209_a4/