Stability Indicators of Nonnegative Matrices: Parametric and Sparse Cases

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 pa...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2023-07, Vol.63 (7), p.1155-1165
Main Author: Razzhevaikin, V. N.
Format: Article
Language:English
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Dynamic stability
Dynamical systems
Epidemiology
General Numerical Method
Indicators
Mathematical analysis
Mathematics
Mathematics and Statistics
Parametric statistics
Sparse matrices
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523070126