• 文献检索
  • 文档翻译
  • 深度研究
  • 学术资讯
  • Suppr Zotero 插件Zotero 插件
  • 邀请有礼
  • 套餐&价格
  • 历史记录
应用&插件
Suppr Zotero 插件Zotero 插件浏览器插件Mac 客户端Windows 客户端微信小程序
定价
高级版会员购买积分包购买API积分包
服务
文献检索文档翻译深度研究API 文档MCP 服务
关于我们
关于 Suppr公司介绍联系我们用户协议隐私条款
关注我们

Suppr 超能文献

核心技术专利：CN118964589B侵权必究
粤ICP备2023148730 号-1Suppr @ 2026

文献检索

告别复杂PubMed语法，用中文像聊天一样搜索，搜遍4000万医学文献。AI智能推荐，让科研检索更轻松。

立即免费搜索

文件翻译

保留排版，准确专业，支持PDF/Word/PPT等文件格式，支持 12+语言互译。

免费翻译文档

深度研究

AI帮你快速写综述，25分钟生成高质量综述，智能提取关键信息，辅助科研写作。

立即免费体验

霍普夫气泡与退化霍普夫分岔的计算机辅助证明

Computer-Assisted Proofs of Hopf Bubbles and Degenerate Hopf Bifurcations.

作者信息

Church Kevin, Queirolo Elena

机构信息

Université de Montréal, Montreal, Canada.

Technische Universität München, Munich, Germany.

出版信息

J Dyn Differ Equ. 2024;36(4):3385-3439. doi: 10.1007/s10884-023-10279-x. Epub 2023 Jul 4.

DOI:10.1007/s10884-023-10279-x
PMID:39554541
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11564292/
Abstract

We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate Hopf bifurcations in ordinary and delay differential equations. We apply the method to rigorously investigate these nonlocal orbit structures in the FitzHugh-Nagumo equation, the extended Lorenz-84 model and a time-delay SI model.

摘要

我们提出了一种计算机辅助方法，以证明常微分方程和时滞微分方程中Hopf气泡和退化Hopf分岔的存在性。我们将该方法应用于严格研究FitzHugh-Nagumo方程、扩展的Lorenz-84模型和一个时滞SI模型中的这些非局部轨道结构。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/4b131942e97f/10884_2023_10279_Fig15_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/725194f82faf/10884_2023_10279_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/40e2e9bf70ad/10884_2023_10279_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/da2d32f5dd00/10884_2023_10279_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/3822f42bc21c/10884_2023_10279_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/69b7831e9a81/10884_2023_10279_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/2acfef6585df/10884_2023_10279_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/8b31d37f2a99/10884_2023_10279_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/62d8b34f4ada/10884_2023_10279_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/0bdc73e58f3f/10884_2023_10279_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/0ca3ce6f31a7/10884_2023_10279_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/59d7e8ba6532/10884_2023_10279_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/afe92e5a198f/10884_2023_10279_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/223604450289/10884_2023_10279_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/dfdf7e036285/10884_2023_10279_Fig14_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/4b131942e97f/10884_2023_10279_Fig15_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/725194f82faf/10884_2023_10279_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/40e2e9bf70ad/10884_2023_10279_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/da2d32f5dd00/10884_2023_10279_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/3822f42bc21c/10884_2023_10279_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/69b7831e9a81/10884_2023_10279_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/2acfef6585df/10884_2023_10279_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/8b31d37f2a99/10884_2023_10279_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/62d8b34f4ada/10884_2023_10279_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/0bdc73e58f3f/10884_2023_10279_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/0ca3ce6f31a7/10884_2023_10279_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/59d7e8ba6532/10884_2023_10279_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/afe92e5a198f/10884_2023_10279_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/223604450289/10884_2023_10279_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/dfdf7e036285/10884_2023_10279_Fig14_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fc12/11564292/4b131942e97f/10884_2023_10279_Fig15_HTML.jpg

相似文献

1
Computer-Assisted Proofs of Hopf Bubbles and Degenerate Hopf Bifurcations.霍普夫气泡与退化霍普夫分岔的计算机辅助证明
J Dyn Differ Equ. 2024;36(4):3385-3439. doi: 10.1007/s10884-023-10279-x. Epub 2023 Jul 4.
2
Andronov-Hopf and Neimark-Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations.时滞微分方程和差分方程中的安德罗诺夫 - 霍普夫分岔与奈马克 - 萨克分岔及其在疾病模型和动物种群模型中的应用
Adv Differ Equ. 2020;2020(1):190. doi: 10.1186/s13662-020-02646-5. Epub 2020 Apr 29.
3
Bifurcation structure of two coupled FHN neurons with delay.具有延迟的两个耦合FHN神经元的分岔结构
Math Biosci. 2015 Dec;270(Pt A):41-56. doi: 10.1016/j.mbs.2015.09.008. Epub 2015 Oct 20.
4
Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.时滞神经网络中的对称性、霍普夫分岔与簇解的出现
Chaos. 2017 Nov;27(11):114316. doi: 10.1063/1.5006921.
5
Numerical analysis of subcritical Hopf bifurcations in the two-dimensional FitzHugh-Nagumo model.二维FitzHugh-Nagumo模型中亚临界霍普夫分岔的数值分析。
Phys Rev E. 2020 Jul;102(1-1):012212. doi: 10.1103/PhysRevE.102.012212.
6
Two-parameter bifurcations analysis of a delayed high-temperature superconducting maglev model with guidance force.具有导向力的延迟高温超导磁悬浮模型的双参数分岔分析
Chaos. 2022 Aug;32(8):083128. doi: 10.1063/5.0104854.
7
Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling.具有延迟耦合的菲茨休-纳古莫可兴奋系统的动力学
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jun;67(6 Pt 2):066222. doi: 10.1103/PhysRevE.67.066222. Epub 2003 Jun 30.
8
Hopf bifurcations in multiple-parameter space of the hodgkin-huxley equations II. Singularity theoretic approach and highly degenerate bifurcations.霍奇金-赫胥黎方程多参数空间中的霍普夫分岔II. 奇点理论方法与高度退化分岔
Biol Cybern. 2000 Mar;82(3):223-9. doi: 10.1007/s004220050022.
9
A Frequency Domain Analysis of the Excitability and Bifurcations of the FitzHugh-Nagumo Neuron Model.一种基于分岔的 FitzHugh-Nagumo 神经元模型的频率域分析
J Phys Chem Lett. 2021 Nov 18;12(45):11005-11013. doi: 10.1021/acs.jpclett.1c03406. Epub 2021 Nov 5.
10
Symmetric bursting behaviors in the generalized FitzHugh-Nagumo model.广义FitzHugh-Nagumo模型中的对称爆发行为。
Biol Cybern. 2013 Aug;107(4):465-76. doi: 10.1007/s00422-013-0559-1. Epub 2013 Jun 26.

本文引用的文献

1
Dynamics of an SIRWS model with waning of immunity and varying immune boosting period.带免疫衰退和免疫增强期变化的 SIRWS 模型动力学。
J Biol Dyn. 2022 Dec;16(1):596-618. doi: 10.1080/17513758.2022.2109766.
2
Quantifying the dose-dependent impact of intracellular amyloid beta in a mathematical model of calcium regulation in xenopus oocyte.定量研究细胞内淀粉样β在爪蟾卵母细胞钙调控数学模型中的剂量依赖性影响。
PLoS One. 2021 Jan 28;16(1):e0246116. doi: 10.1371/journal.pone.0246116. eCollection 2021.
3
A mathematical model for the effects of amyloid beta on intracellular calcium.
淀粉样β蛋白对细胞内钙的影响的数学模型。
PLoS One. 2018 Aug 22;13(8):e0202503. doi: 10.1371/journal.pone.0202503. eCollection 2018.
4
Bursting endemic bubbles in an adaptive network.在自适应网络中打破地方性爆发泡沫。
Phys Rev E. 2018 Apr;97(4-1):042306. doi: 10.1103/PhysRevE.97.042306.
5
Modeling calcium waves in an anatomically accurate three-dimensional parotid acinar cell.在具有精确解剖结构的三维腮腺腺泡细胞中模拟钙波。
J Theor Biol. 2017 Apr 21;419:383-393. doi: 10.1016/j.jtbi.2016.04.030. Epub 2016 May 4.
6
Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience.神经科学中振荡网络动力学的数学框架
J Math Neurosci. 2016 Dec;6(1):2. doi: 10.1186/s13408-015-0033-6. Epub 2016 Jan 6.