Stabilization of cycles for difference equations with a noisy PF control

Stabilization of cycles for difference equations with a noisy PF control

WoS Article

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.

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.

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

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

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

2021

21.02.2020

Elsevier

OXFORD

0005-1098

AUTOMATICA

115

1

United States of America

1

8

8

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

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

Rodkina-Automatica
stabilization_cycles_preprint