title: Combinatorial-topological framework for the analysis of global dynamics.
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.
authors.affiliation: Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA. bushjc@math.rutgers.edu
authors.forename: Justin
authors.initials: J
authors.lastname: Bush
authors.forename: Marcio
authors.initials: M
authors.lastname: Gameiro
authors.forename: Shaun
authors.initials: S
authors.lastname: Harker
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Kokubu
authors.forename: Konstantin
authors.initials: K
authors.lastname: Mischaikow
authors.forename: Ippei
authors.initials: I
authors.lastname: Obayashi
authors.forename: Paweł
authors.initials: P
authors.lastname: Pilarczyk