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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 7, Pages 1061–1072
DOI: https://doi.org/10.31857/S004446692307013X (Mi zvmmf11579) 		 
General numerical methods

Stability indicators of nonnegative matrices: Parametric and sparse cases

V. N. Razzhevaikin

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 119333, Moscow, Russia
DOI: https://doi.org/10.31857/S004446692307013X
Abstract: Methods for the algorithmic construction of stability indicators of nonnegative matrices is described, and the application of these indicators to problems of modern mathematical biology and epidemiology is discussed. Specific features of such indicators when they are applied to problems about the parametric loss of stability of trivial equilibrium states of discrete dynamical systems are pointed out. Estimates of the efficiency of algorithms based on the proposed methods for the case of systems determined by sparse matrices are given. Examples of using the constructed algorithms for such systems are discussed.
Key words: nonnegative matrix, stability indicator, discrete dynamical system, parametric system, sparse matrix.
Received: 22.06.2022
Revised: 06.02.2023
Accepted: 30.03.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 7, Pages 1155–1165
DOI: https://doi.org/10.1134/S0965542523070126
Bibliographic databases:
Document Type: Article
UDC: 519.614.2
Language: Russian
Citation: V. N. Razzhevaikin, “Stability indicators of nonnegative matrices: Parametric and sparse cases”, Zh. Vychisl. Mat. Mat. Fiz., 63:7 (2023), 1061–1072; Comput. Math. Math. Phys., 63:7 (2023), 1155–1165
Citation in format AMSBIB
\Bibitem{Raz23}
\by V.~N.~Razzhevaikin
\paper Stability indicators of nonnegative matrices: Parametric and sparse cases
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 7
\pages 1061--1072
\mathnet{http://mi.mathnet.ru/zvmmf11579}
\crossref{https://doi.org/10.31857/S004446692307013X}
\elib{https://elibrary.ru/item.asp?id=54238529}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 7
\pages 1155--1165
\crossref{https://doi.org/10.1134/S0965542523070126}
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