Physics
Scientific paper
Jan 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011njph...13a3041w&link_type=abstract
New Journal of Physics, Volume 13, Issue 1, pp. 013041 (2011).
Physics
Scientific paper
Random multistate networks, generalizations of the Boolean Kauffman networks, are generic models for complex systems of interacting agents. Depending on their mean connectivity, these networks exhibit ordered as well as chaotic behavior with a critical boundary separating both regimes. Typically, the nodes of these networks are assigned single discrete states. Here, we describe nodes by fuzzy numbers, i.e. vectors of degree-of-membership (DOM) functions specifying the degree to which the nodes are in each of their discrete states. This allows our models to deal with imprecision and uncertainties. Compatible update rules are constructed by expressing the update rules of the multistate network in terms of Boolean operators and generalizing them to fuzzy logic (FL) operators. The standard choice for these generalizations is the Gödel FL, where AND and OR are replaced by the minimum and maximum of two DOMs, respectively. In mean-field approximations we are able to analytically describe the percolation and asymptotic distribution of DOMs in random Gödel FL networks. This allows us to characterize the different dynamic regimes of random multistate networks in terms of FL. In a low-dimensional example, we provide explicit computations and validate our mean-field results by showing that they agree well with network simulations.
Theis Fabian J.
Wittmann Dominik M.
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