Detail publikace

Stabilization of cycles for difference equations with a noisy PF control

BRAVERMAN, E. DIBLÍK, J. RODKINA, A. ŠMARDA, Z.

Originální název

Stabilization of cycles for difference equations with a noisy PF control

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

Difference equations, such as a Ricker map, for an increased value of the parameter, experience instability of the positive equilibrium and transition to deterministic chaos. To achieve stabilization, various methods can be applied. Proportional Feedback control suggests a proportional reduction of the state variable at every kth step. First, if k not equal 1, a cycle is stabilized rather than an equilibrium. Second, the equation can incorporate an additive noise term, describing the variability of the environment, as well as multiplicative noise corresponding to possible deviations in the control intensity. The present paper deals with both issues, it justifies a possibility of getting a stable blurred k-cycle. Presented examples include the Ricker model, as well as equations with unbounded f, such as the bobwhite quail population models. Though the theoretical results justify stabilization for either multiplicative or additive noise only, numerical simulations illustrate that a blurred cycle can be stabilized when both multiplicative and additive noises are involved. (C) 2020 Elsevier Ltd. All rights reserved.

Klíčová slova

Stochastic difference equations; Proportional feedback control; Multiplicative noise; Additive noise; Ricker map; Stable cycles

Autoři

BRAVERMAN, E.; DIBLÍK, J.; RODKINA, A.; ŠMARDA, Z.

Vydáno

21. 2. 2020

Nakladatel

Elsevier

Místo

OXFORD

ISSN

0005-1098

Periodikum

AUTOMATICA

Ročník

115

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

8

Strany počet

8

URL

https://www.sciencedirect.com/science/article/pii/S0005109820300601

Plný text v Digitální knihovně

http://hdl.handle.net/11012/195668

BibTex

@article{BUT163803,
  author="Elena {Braverman} and Josef {Diblík} and Alexandra {Rodkina} and Zdeněk {Šmarda}",
  title="Stabilization of cycles for difference equations with a noisy PF control",
  journal="AUTOMATICA",
  year="2020",
  volume="115",
  number="1",
  pages="1--8",
  doi="10.1016/j.automatica.2020.108862",
  issn="0005-1098",
  url="https://www.sciencedirect.com/science/article/pii/S0005109820300601"
}