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Combinatorial-topological framework for the analysis of global dynamics
Justin Bush1, Marcio Gameiro, Shaun Harker
1Department 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
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.
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