Combinatorial-topological framework for the analysis of global dynamics

摘要

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.