TY  - JOUR
ID  - Dzhalladova2019
LB  - Dzhalladova2019
AU  - Dzhalladova, Irada
AU  - Růžičková, Miroslava
TI  - Dynamic system with random structure for modeling security and risk management in cyberspace
ST  - Dynamic system with random structure for modeling security and risk management in cyberspace
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 1
SP  - 23
EP  - 37
DO  - https://doi.org/10.7494/OpMath.2019.39.1.23
UR  - https://doi.org/10.7494/OpMath.2019.39.1.23
AB  - 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.
KW  - semi-Markov chain
KW  - random transformation of solutions
KW  - the Lyapunov function
KW  - \(L_{2}\)-stability
KW  - systems of difference equations
KW  - jumps of solutions
KW  - cybersecurity
SN  - 1232-9274
ER  -