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

Kaname Matsue

doi:10.1137/080742944

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

Kaname Matsue

Research output: Contribution to journal › Article › peer-review

2 Citations (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 language	English
Pages (from-to)	325-359
Number of pages	35
Journal	SIAM Journal on Applied Dynamical Systems
Volume	10
Issue number	1
DOIs	https://doi.org/10.1137/080742944
Publication status	Published - 2011
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Modelling and Simulation

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10.1137/080742944

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

Abstract

All Science Journal Classification (ASJC) codes

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