A method for finding aggregated representations of linear dynamical systems
Journal article, 2010
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 with n states correspond to a set of n eigenvectors of the dynamics matrix such that these respect the same permutation symmetry with n orbits. We exemplify the applicability of the algorithm by employing it to identify coarse grained representations of cellular automata.
complexity
prediction
aggregated Markov chains
lumpability
cellular-automata
network clustering
weak lumpability
markov-chains
aggregation of variables
state space reduction
variables
reduction
hierarchical networks
selection
cellular automata
Hierarchical dynamics
Author
Olof Görnerup
Chalmers, Energy and Environment, Physical Resource Theory
Martin Nilsson Jacobi
Chalmers, Energy and Environment, Physical Resource Theory
Advances in Complex Systems
0219-5259 (ISSN)
Vol. 13 2 199-215Subject Categories
Physical Sciences
DOI
10.1142/S0219525910002542