Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on e cient graph algorithms and 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-dimensiona...

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Detalhes bibliográficos
Autor principal: Bush, Justin (author)
Outros Autores: Gameiro, Marcio (author), Harker, Shaun (author), Kokubu, Hiroshi (author), Mischaikow, Konstantin (author), Obayashi, Ippei (author), Pilarczyk, Pawel (author)
Formato: article
Idioma:eng
Publicado em: 2012
Assuntos:
Dynamical system
Morse decomposition
Conley index
Grid decomposition
Graph algorithms
Rigorous numerics
Science & Technology
Texto completo:http://hdl.handle.net/1822/21112
País:Portugal
Oai:oai:repositorium.sdum.uminho.pt:1822/21112
Descrição
Resumo:We discuss an algorithmic framework based on e cient graph algorithms and 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 and parameter space, and show two sample applications.

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