Rigorous verification of bifurcations of differential equations via the conley index theory

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We propose a new approach for capturing bifurcations of (semi)flows by using a topological tool, the Conley index. We can apply this concept to capture bifurcations with rigorous numerics. As an example, we consider the dynamics generated by the Swift-Hohenberg PDE and show that a pitchfork-like bifurcation occurs in a certain region.

Original languageEnglish
Pages (from-to)325-359
Number of pages35
JournalSIAM Journal on Applied Dynamical Systems
Volume10
Issue number1
DOIs
Publication statusPublished - May 10 2011
Externally publishedYes

Fingerprint

Conley Index
Index Theory
Bifurcation (mathematics)
Differential equations
Bifurcation
Differential equation
Semiflow
Numerics

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modelling and Simulation

Cite this

Rigorous verification of bifurcations of differential equations via the conley index theory. / Matsue, Kaname.

In: SIAM Journal on Applied Dynamical Systems, Vol. 10, No. 1, 10.05.2011, p. 325-359.

Research output: Contribution to journalArticle

@article{a2b9beab7d1e4cca8397a7c12641f3b9,
title = "Rigorous verification of bifurcations of differential equations via the conley index theory",
abstract = "We propose a new approach for capturing bifurcations of (semi)flows by using a topological tool, the Conley index. We can apply this concept to capture bifurcations with rigorous numerics. As an example, we consider the dynamics generated by the Swift-Hohenberg PDE and show that a pitchfork-like bifurcation occurs in a certain region.",
author = "Kaname Matsue",
year = "2011",
month = "5",
day = "10",
doi = "10.1137/080742944",
language = "English",
volume = "10",
pages = "325--359",
journal = "SIAM Journal on Applied Dynamical Systems",
issn = "1536-0040",
publisher = "Society of Industrial and Applied Mathematics",
number = "1",

}

TY - JOUR

T1 - Rigorous verification of bifurcations of differential equations via the conley index theory

AU - Matsue, Kaname

PY - 2011/5/10

Y1 - 2011/5/10

N2 - We propose a new approach for capturing bifurcations of (semi)flows by using a topological tool, the Conley index. We can apply this concept to capture bifurcations with rigorous numerics. As an example, we consider the dynamics generated by the Swift-Hohenberg PDE and show that a pitchfork-like bifurcation occurs in a certain region.

AB - We propose a new approach for capturing bifurcations of (semi)flows by using a topological tool, the Conley index. We can apply this concept to capture bifurcations with rigorous numerics. As an example, we consider the dynamics generated by the Swift-Hohenberg PDE and show that a pitchfork-like bifurcation occurs in a certain region.

UR - http://www.scopus.com/inward/record.url?scp=79955651815&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955651815&partnerID=8YFLogxK

U2 - 10.1137/080742944

DO - 10.1137/080742944

M3 - Article

VL - 10

SP - 325

EP - 359

JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

SN - 1536-0040

IS - 1

ER -