Bifurcation Analysis of Bogdanov–Takens Bifurcations in Delay Differential Equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-30 DOI:10.1137/22m1527532

M. M. Bosschaert, Yu. A. Kuznetsov

引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 553-591, March 2024.
Abstract. In this paper, we will perform the parameter-dependent center manifold reduction near the generic and transcritical codimension two Bogdanov–Takens bifurcation in classical delay differential equations. Using an approximation to the homoclinic solutions derived with a generalized Lindstedt–Poincaré method, we develop a method to initialize the continuation of the homoclinic bifurcation curves emanating from these points. The normal form transformation is derived in the functional analytic perturbation framework for dual semigroups (sun-star calculus) using a normalization technique based on the Fredholm alternative. The obtained expressions give explicit formulas, which have been implemented in the freely available bifurcation software package DDE-BifTool. The effectiveness is demonstrated on various models

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延迟微分方程中的波格丹诺夫-塔肯斯分岔分析

SIAM 应用动力系统期刊》，第 23 卷第 1 期，第 553-591 页，2024 年 3 月。摘要本文将在经典延迟微分方程中的一般和跨临界二维 Bogdanov-Takens 分岔附近进行与参数相关的中心流形还原。利用广义林斯特-普因卡雷方法推导出的同次元解近似值，我们开发了一种方法来初始化从这些点出发的同次元分岔曲线的延续。利用基于弗雷德霍姆替代法的归一化技术，在对偶半群（太阳星微积分）的函数分析扰动框架中推导出了正态形式变换。得到的表达式给出了明确的公式，这些公式已在免费提供的分岔软件包 DDE-BifTool 中实现。在各种模型上证明了其有效性

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.