Combinatorial-topological framework for the analysis of global dynamics

Justin Bush, Marcio Gameiro, Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow, Ippei Obayashi, Paweł Pilarczyk

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

We discuss an algorithmic framework based on efficient graph algorithms algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space parameter space, show two sample applications.

Original languageEnglish
Article number047508
JournalChaos
Volume22
Issue number4
DOIs
Publication statusPublished - 2012 Oct 4

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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