Spatiotemporal Patterns in a Lengyel–Epstein Model Near a Turing–Hopf Singular Point

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-03-01 DOI:10.1137/23m1552668

Shuangrui Zhao, Pei Yu, Hongbin Wang

{"title":"Spatiotemporal Patterns in a Lengyel–Epstein Model Near a Turing–Hopf Singular Point","authors":"Shuangrui Zhao, Pei Yu, Hongbin Wang","doi":"10.1137/23m1552668","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 338-361, April 2024. <br/> Abstract. In this paper, a study is carried out on the spatiotemporal dynamics of a Lengyel–Epstein model describing the chlorite-iodine-malonic-acid (CIMA) reaction with time delay and the Neumann boundary condition in a two-dimensional region. The existences for Turing, Hopf, Turing–Turing, Turing–Hopf, and Bogdanov–Takens bifurcations are derived by analyzing the dispersion relation between eigenvalues and wave numbers. In particular, to study the dynamics around a Turing–Hopf bifurcation singularity, the amplitude equations near a codimension-two bifurcation point are derived by employing the weakly nonlinear analysis method. Different spatiotemporal patterns for the system in parameter space are classified and various patterns identified, including spatially homogeneous periodic solutions, mixed mode, coexistence mode, bistable phenomenon, square, hexagon, black eye, two-phase oscillating staggered hexagon lattice, and other complex spatiotemporal patterns. The theoretical predictions are verified by numerical simulations showing an excellent agreement with many reported experiment results not only in chemistry but also in physics and biology. Results presented in this article reveal the mechanism of generating the spatiotemporal patterns of the CIMA reaction.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1552668","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 338-361, April 2024.
Abstract. In this paper, a study is carried out on the spatiotemporal dynamics of a Lengyel–Epstein model describing the chlorite-iodine-malonic-acid (CIMA) reaction with time delay and the Neumann boundary condition in a two-dimensional region. The existences for Turing, Hopf, Turing–Turing, Turing–Hopf, and Bogdanov–Takens bifurcations are derived by analyzing the dispersion relation between eigenvalues and wave numbers. In particular, to study the dynamics around a Turing–Hopf bifurcation singularity, the amplitude equations near a codimension-two bifurcation point are derived by employing the weakly nonlinear analysis method. Different spatiotemporal patterns for the system in parameter space are classified and various patterns identified, including spatially homogeneous periodic solutions, mixed mode, coexistence mode, bistable phenomenon, square, hexagon, black eye, two-phase oscillating staggered hexagon lattice, and other complex spatiotemporal patterns. The theoretical predictions are verified by numerical simulations showing an excellent agreement with many reported experiment results not only in chemistry but also in physics and biology. Results presented in this article reveal the mechanism of generating the spatiotemporal patterns of the CIMA reaction.

查看原文本刊更多论文

靠近图灵-霍普夫奇点的伦盖尔-爱泼斯坦模型中的时空模式

SIAM 应用数学杂志》第 84 卷第 2 期第 338-361 页，2024 年 4 月。摘要本文研究了二维区域内带时延和新曼边界条件的氯碘丙二酸（CIMA）反应的 Lengyel-Epstein 模型的时空动力学。通过分析特征值和波数之间的离散关系，推导出图灵分岔、霍普夫分岔、图灵-图灵分岔、图灵-霍普夫分岔和波格丹诺夫-塔肯斯分岔的存在。特别是，为了研究图灵-霍普夫分岔奇点周围的动力学，采用弱非线性分析方法推导出了二维分岔点附近的振幅方程。对系统在参数空间中的不同时空模式进行了分类，确定了各种模式，包括空间均匀周期解、混合模式、共存模式、双稳态现象、正方形、六边形、黑眼、两相振荡交错六边形晶格以及其他复杂时空模式。数值模拟验证了理论预测，结果表明与许多已报道的实验结果非常吻合，不仅在化学领域，在物理学和生物学领域也是如此。本文介绍的结果揭示了 CIMA 反应时空模式的生成机制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.