@article{531be520697147338be62815fd550d38,
title = "Combinatorial-topological framework for the analysis of global dynamics",
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.",
author = "Justin Bush and Marcio Gameiro and Shaun Harker and Hiroshi Kokubu and Konstantin Mischaikow and Ippei Obayashi and Pawe{\l} Pilarczyk",
note = "Funding Information: M.G. acknowledges the support of Fapesp Processo 2010/00875-9 and CNPq Processo 306453/2009-6. H.K. acknowledges the support of Ministry of Education, Science, Technology, Culture and Sports, Japan, Grant-in-Aid for Scientific Research No. 21340035. The work of K.M., S.H., and J.B. was partially supported by NSF Grants DMS-0915019 and CBI-0835621 and by contracts from DARPA and AFOSR. P.P. acknowledges the support from the E.U. and Portuguese national funds received through Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia (FCT), project FCOMP-01-0124-FEDER-010645 (Ref. FCT PTDC/MAT/098871/2008) and Est-C/MAT/UI0013/2011. ",
year = "2012",
month = oct,
day = "4",
doi = "10.1063/1.4767672",
language = "English",
volume = "22",
journal = "Chaos",
issn = "1054-1500",
publisher = "American Institute of Physics Publising LLC",
number = "4",
}