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DIBLÍK, J. RODKINA, A. ŠMARDA, Z.
Originální název
On local stability of stochastic delay nonlinear discrete systems with state-dependent noise.
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
angličtina
Originální abstrakt
We examine the local stability of solutions of a delay stochastic nonlinear difference equation with deterministic and state-dependent Gaussian perturbations. We apply the degenerate Lyapunov–Krasovskii functional technique and construct a sequence of events, each term of which is defined by a bound on a normally distributed random variable. Local stability holds on the intersection of these events, which has probability at least 1- γ, γ ∈ (0, 1). This probability can be made arbitrarily high by choosing the initial value sufficiently small. We also present a generalization to systems where a condition for stability is expressed in terms of the diagonal part of the unperturbed system, and computer simulations which illustrate our results.
Klíčová slova
Nonlinear stochastic difference equations; Local stability; State dependent perturbations
Autoři
DIBLÍK, J.; RODKINA, A.; ŠMARDA, Z.
Vydáno
25. 1. 2020
Nakladatel
Elsevier
Místo
PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
ISSN
1873-5649
Periodikum
Applied Mathematics and Computation
Ročník
374
Číslo
125019
Stát
Spojené státy americké
Strany od
1
Strany do
15
Strany počet
URL
https://www-sciencedirect-com.ezproxy.lib.vutbr.cz/science/article/pii/S0096300319310112
BibTex
@article{BUT163757, author="Josef {Diblík} and Alexandra {Rodkina} and Zdeněk {Šmarda}", title="On local stability of stochastic delay nonlinear discrete systems with state-dependent noise.", journal="Applied Mathematics and Computation", year="2020", volume="374", number="125019", pages="1--15", doi="10.1016/j.amc.2019.125019", issn="1873-5649", url="https://www-sciencedirect-com.ezproxy.lib.vutbr.cz/science/article/pii/S0096300319310112" }