Adaptive rewiring of links in a network: Jammed states

Abstract

We investigate stationary states produced within the limited version of the Axelrod model, where the dynamics is reduced to the rewiring, and the copying of states is switched off. The work function W is defined as the sum of Hamming distances between linked nodes. The rewiring occurs only if the work function does not increase. The state of a node is a chain of symbols, with the chain length F, and each symbol can admit one of q values. Initially, N actors are placed at randomly selected nodes-states, and L links are distributed between actors. Numerical calculations allow to identify ranges of parameters N,L,F,q where, for a given configuration of occupied states, W remains above its minimal value. These metastable configurations, termed here as jammed states, are shown to be abundant for L close to its limit values 1 and N(N−1)∕2−1, and rare or absent for intermediate connectivities. The simulations allow to evaluate the role of basins of attraction of the jammed states.