A SPECTRAL METHOD FOR AGGREGATING VARIABLES IN LINEAR DYNAMICAL SYSTEMS WITH APPLICATION TO CELLULAR AUTOMATA RENORMALIZATION

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

Advances in Complex Systems (ACS), 2009, vol. 12, issue 02, pages 131-155

Abstract: We present a method for identifying coarse-grained dynamics through aggregation of variables or states in linear dynamical systems. The condition for aggregation is expressed as a permutation symmetry of a set of dual eigenvectors of the matrix that defines the dynamics. The applicability of the condition is illustrated in examples from three different generic classes of reducible Markov chains: systems consisting of independent subsystems, dynamics with symmetries, and nearly decoupled Markov chains. Furthermore we show how the method can be used to coarse-grain cellular automata.

Keywords: Lumpability; aggregated Markov chains; aggregation of variables; aggregated linear dynamics; quotient processes; state space reduction; renormalization; coarse-graining; cellular automata (search for similar items in EconPapers)
Date: 2009

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