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

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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

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modelling and Simulation

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