Anomalous lifetime distributions and topological traps in ordering dynamics

Abstract

We address the role of community structure of an interaction network in ordering dynamics, as well as associated forms of metastability. We consider the voter and AB model dynamics in a network model which mimics social interactions. The AB model includes an intermediate state between the two excluding options of the voter model. For the voter model we find dynamical metastable disordered states with a characteristic mean lifetime. However, for the AB dynamics we find a power law distribution of the lifetime of metastable states, so that the mean lifetime is not representative of the dynamics. These trapped metastable states, which can order at all time scales, originate in the mesoscopic network structure.

7 pages; 6 figures

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Cited by in corpus (27)

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• Analytical Solution of the Voter Model on Disordered Networks
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• Influence of geography on language competition
• Consensus and ordering in language dynamics
• Dynamics of latent voters
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• Agent Based Models of Language Competition: Macroscopic descriptions and Order-Disorder transitions
• Modularity produces small-world networks with dynamical time-scale separation
• Modeling two-language competition dynamics
• Rare region effects in the contact process on networks
• Dynamics on networks: competition of temporal and topological correlations
• Broad lifetime distributions for ordering dynamics in complex networks
• Phase of Ising spins on modular networks analogous to social polarization
• Rare regions of the Susceptible Infected Susceptible model on Barabási-Albert networks
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• Naming Game on Adaptive Weighted Networks
• Voter model on a directed network: Role of bidirectional opinion exchanges
• Dynamics of link states in complex networks: The case of a majority rule
• Coupling of link- and node-ordering in the coevolving voter model
• A model of competition among more than two languages
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• Voter model on networks partitioned into two cliques of arbitrary sizes
• Moment-Closure Approximations for Discrete Adaptive Networks
• Language change in a multiple group society
• Slow dynamics of the contact process on complex networks