Combinatorial-topological framework for the analysis of global dynamics

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: Chaos; v. 22, n. 4 DEC 2012.
• Web of Science Citations: 22

Abstract

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)

• FAPESP's process: 10/00875-9 - Topological methods and rigorous numerics for bifurcations of dynamical systems
• Grantee: Marcio Fuzeto Gameiro
• Support Opportunities: Regular Research Grants