Publication result detail

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

DIBLÍK, J.; RODKINA, A.; ŠMARDA, Z.

Original Title

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

English Title

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

Type

WoS Article

Original Abstract

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.

English abstract

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.

Keywords

Nonlinear stochastic difference equations; Local stability; State dependent perturbations

Key words in English

Nonlinear stochastic difference equations; Local stability; State dependent perturbations

Authors

DIBLÍK, J.; RODKINA, A.; ŠMARDA, Z.

RIV year

2021

Released

25.01.2020

Publisher

Elsevier

Location

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

ISBN

1873-5649

Periodical

APPLIED MATHEMATICS AND COMPUTATION

Volume

374

Number

125019

State

United States of America

Pages from

1

Pages to

15

Pages count

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"
}