Publication detail

Stabilization of cycles for difference equations with a noisy PF control

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

Original Title

Stabilization of cycles for difference equations with a noisy PF control

English Title

Stabilization of cycles for difference equations with a noisy PF control

Type

journal article in Web of Science

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

21.02.2020

Publisher

Elsevier

Location

OXFORD

ISBN

0005-1098

Periodical

AUTOMATICA

Year of study

115

Number

1

State

US

Pages from

1

Pages to

8

Pages count

8

URL

Full text in the Digital Library

Documents

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",
  annote="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.",
  address="Elsevier",
  chapter="163803",
  doi="10.1016/j.automatica.2020.108862",
  howpublished="online",
  institution="Elsevier",
  number="1",
  volume="115",
  year="2020",
  month="february",
  pages="1--8",
  publisher="Elsevier",
  type="journal article in Web of Science"
}