Detail publikačního výsledku

On local stability of stochastic delay nonlinear discrete systems with state-dependent noise.

DIBLÍK, J.; RODKINA, A.; ŠMARDA, Z.

Originální název

On local stability of stochastic delay nonlinear discrete systems with state-dependent noise.

Anglický název

On local stability of stochastic delay nonlinear discrete systems with state-dependent noise.

Druh

Článek WoS

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.

Anglický 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

Klíčová slova v angličtině

Nonlinear stochastic difference equations; Local stability; State dependent perturbations

Autoři

DIBLÍK, J.; RODKINA, A.; ŠMARDA, Z.

Rok RIV

2021

Vydáno

25.01.2020

Nakladatel

Elsevier

Místo

PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND

ISSN

1873-5649

Periodikum

APPLIED MATHEMATICS AND COMPUTATION

Svazek

374

Číslo

125019

Stát

Spojené státy americké

Strany od

1

Strany do

15

Strany počet

15

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="0096-3003",
  url="https://www-sciencedirect-com.ezproxy.lib.vutbr.cz/science/article/pii/S0096300319310112"
}