A rigorous numerical method for the global analysis of infinite-dimensional discrete dynamical systems

S. Day, O. Junge, K. Mischaikow

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

We present a numerical method to prove certain statements about the global dynamics of infinite-dimensional maps. The method combines set-oriented numerical tools for the computation of invariant sets and isolating neighborhoods, the Conley index theory, and analytic considerations. It not only allows for the detection of a certain dynamical behavior, but also for a precise computation of the corresponding invariant sets in phase space. As an example computation we show the existence of period points, connecting orbits, and chaotic dynamics in the Kot-Schaffer growth-dispersal model for plants.

Original languageEnglish (US)
Pages (from-to)117-160
Number of pages44
JournalSIAM Journal on Applied Dynamical Systems
Volume3
Issue number2
DOIs
StatePublished - May 19 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation

Keywords

  • Conley index
  • Dynamical system
  • Infinite-dimensional
  • Numercial method

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