A METHOD FOR FINDING AGGREGATED REPRESENTATIONS OF LINEAR DYNAMICAL SYSTEMS

Olof Görnerup () and Martin Nilsson Jacobi ()
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Olof Görnerup: Complex Systems Group, Department of Energy and Environment, Chalmers University of Technology, 412 96 Göteborg, Sweden
Martin Nilsson Jacobi: Complex Systems Group, Department of Energy and Environment, Chalmers University of Technology, 412 96 Göteborg, Sweden

Advances in Complex Systems (ACS), 2010, vol. 13, issue 02, 199-215

Abstract: A central problem in the study of complex systems is to identify hierarchical and intertwined dynamics. A hierarchical level is defined as an aggregation of the system's variables such that the aggregation induces its own closed dynamics. In this paper, we present an algorithm that finds aggregations of linear dynamical systems, e.g. including Markov chains and diffusion processes on weighted and directed networks. The algorithm utilizes that a valid aggregation withnstates correspond to a set ofneigenvectors of the dynamics matrix such that these respect the same permutation symmetry withnorbits. We exemplify the applicability of the algorithm by employing it to identify coarse grained representations of cellular automata.

Keywords: Hierarchical dynamics; aggregation of variables; lumpability; aggregated Markov chains; state space reduction; hierarchical networks; network clustering; cellular automata (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0219525910002542

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