Controlling pulse stability in singularly perturbed reaction-diffusion systems

被引：1

作者：

Veerman, F. ^{[1
]}

Schneider, I. ^{[2
]}

机构：

[1] Leiden Univ, Math Inst, Niels Bohrweg 1, NL-2333 CA Leiden, Netherlands

[2] Univ Rostock, Inst Math, Ulmenstr 69, D-18057 Rostock, Germany

来源：

CHAOS | 2023年 / 33卷 / 08期

关键词：

FEEDBACK-CONTROL; BIFURCATIONS; PATTERNS; EQUATION; CHAOS;

D O I：

10.1063/5.0152695

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to investigate the use of Pyragas control on the stability of stationary, localized coherent structures in a general class of two-component, singularly perturbed, reaction-diffusion systems. We use noninvasive Pyragas-like proportional feedback control to stabilize a singular pulse solution to a two-component, singularly perturbed reaction-diffusion system. We show that in a significant region of parameter space, the control can be adjusted to stabilize an otherwise unstable pulse.

引用

页数：11

共 50 条

[1] STABILITY OF SINGULARLY PERTURBED SOLUTIONS TO SYSTEMS OF REACTION-DIFFUSION EQUATIONS
NISHIURA, Y
FUJII, H
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1987, 18 (06) : 1726 - 1770
[2] STABILITY THEOREM FOR SINGULARLY PERTURBED SOLUTIONS TO SYSTEMS OF REACTION-DIFFUSION EQUATIONS
NISHIURA, Y
FUJII, H
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1985, 61 (10) : 329 - 332
[3] Stability of spatially periodic pulse patterns in a class of singularly perturbed reaction-diffusion equations
van der Ploeg, H
Doelman, A
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2005, 54 (05) : 1219 - 1301
[4] Breathing pulses in singularly perturbed reaction-diffusion systems
Veerman, Frits
NONLINEARITY, 2015, 28 (07) : 2211 - 2246
[5] Breathing pulses in singularly perturbed reaction-diffusion systems
Veerman, Frits
NONLINEARITY, 2017, 30 (03) : C1 - +
[6] Singularly Perturbed Reaction-Diffusion Problems as First order systems
Franz, Sebastian
JOURNAL OF SCIENTIFIC COMPUTING, 2021, 89 (02)
[7] MULTILEVEL SCHWARZ PRECONDITIONERS FOR SINGULARLY PERTURBED SYMMETRIC REACTION-DIFFUSION SYSTEMS
Lorca, Jose Pablo Lucero
Kanschat, Guido
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2021, 54 : 89 - 107
[8] Multilevel schwarz preconditioners for singularly perturbed symmetric reaction-diffusion systems
LORCA, JOSÉ PABLO LUCERO
KANSCHAT, GUIDO
Electronic Transactions on Numerical Analysis, 2021, 54 : 89 - 107
[9] Spikes for singularly perturbed reaction-diffusion systems and carrier's problem
Ward, MJ
DIFFERENTIAL EQUATIONS & ASYMPTOTIC THEORY MATHEMATICAL PHYSICS, 2004, 2 : 100 - 188
[10] Pulses in singularly perturbed reaction-diffusion systems with slowly mixed nonlinearity
Chen, Yuanxian
Cai, Yuhua
Shen, Jianhe
CHAOS, 2024, 34 (11)

← 1 2 3 4 5 →