Dynamic system with random structure for modeling security and risk management in cyberspace | Zendy

Ірада Джалладова | Zendy; Miroslava Růžičková | Zendy

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Dynamic system with random structure for modeling security and risk management in cyberspace

Author(s) -

Ірада Джалладова,

Miroslava Růžičková

Publication year - 2018

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2019.39.1.23

Subject(s) - cyberspace , mathematics , stability (learning theory) , markov chain , lyapunov function , mathematical optimization , computer science , the internet , statistics , physics , nonlinear system , quantum mechanics , machine learning , world wide web

We deal with the investigation of \(L_{2}\)-stability of the trivial solution to the system of difference equations with coefficients depending on a semi-Markov chain. In our considerations, random transformations of solutions are assumed. Necessary and sufficient conditions for \(L_{2}\)-stability of the trivial solution to such systems are obtained. A method is proposed for constructing Lyapunov functions and the conditions for its existence are justified. The dynamic system and methods discussed in the paper are very well suited for use as models for protecting information in cyberspace.

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