Combinatorial-topological framework for the analysis of global dynamics

Autor(es)

Bush, Justin ^[1] ; Gameiro, Marcio ^[2] ; Harker, Shaun ^[1] ; Kokubu, Hiroshi ^[3] ; Mischaikow, Konstantin ^{[1, 4]} ; Obayashi, Ippei ^[3] ; Pilarczyk, Pawel ^[5]

Afiliação do(s) autor(es)

^[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 - USA

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[3] Kyoto Univ, Dept Math, JST CREST, Kyoto 6068502 - Japan

^[4] Rutgers State Univ, BioMaPS, Piscataway, NJ 08854 - USA

^[5] Univ Minho, Ctr Math, P-4710057 Braga - Portugal

• Tipo de documento: Artigo Científico
• Fonte: Chaos; v. 22, n. 4 DEC 2012.
• Citações Web of Science: 22

Resumo

We discuss an algorithmic framework based on efficient 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. (C) 2012 American Institute of Physics. {[}http://dx.doi.org/10.1063/1.4767672] (AU)

• Processo FAPESP: 10/00875-9 - Métodos topológicos e numéricos rigorosos para bifurcações em sistemas dinâmicos
• Beneficiário: Marcio Fuzeto Gameiro
• Modalidade de apoio: Auxílio à Pesquisa - Regular