Unanimity Rule on networks

Abstract

We introduce a model for innovation-, evolution- and opinion dynamics whose spreading is dictated by unanimity rules, i.e. a node will change its (binary) state only if all of its neighbours have the same corresponding state. It is shown that a transition takes place depending on the initial condition of the problem. In particular, a critical number of initially activated nodes is needed so that the whole system gets activated in the long-time limit. The influence of the degree distribution of the nodes is naturally taken into account. For simple network topologies we solve the model analytically, the cases of random, small-world and scale-free are studied in detail.

7 pages 4 figs

References in corpus (20)

• Emergence of scaling in random networks
• Epidemic spreading in scale-free networks
• Organization of Growing Random Networks
• Voter Model on Heterogeneous Graphs
• Universal behavior in a generalized model of contagion
• Dynamics of Majority Rule
• Cascade Dynamics of Multiplex Propagation
• Nonequilibrium phase transition in a model for social influence
• Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution
• Incomplete ordering of the voter model on small-world networks
• Coarsening and persistence in the voter model
• Comparison of voter and Glauber ordering dynamics on networks
• Majority versus minority dynamics: Phase transition in an interacting two-state spin system
• Majority Model on a network with communities
• Continuum time limit and stationary states of the Minority Game
• Divergent Time Scale in Axelrod Model Dynamics
• Sociophysics Simulations II: Opinion Dynamics
• The phase transition in random catalytic sets
• How does degree heterogeneity affect an order-disorder transition?
• Cooperative Parrondo's Games on a Two-dimensional Lattice

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• Opinion dynamics on directed small-world networks
• Complex dynamics of a nonlinear voter model with contrarian agents
• Propagation on networks: an exact alternative perspective
• Equation-Free Multiscale Computations in Social Networks: from Agent-based Modelling to Coarse-grained Stability and Bifurcation Analysis
• Kauffman Boolean model in undirected scale free networks
• Opinion formation models on a gradient
• Solution of the Unanimity Rule on exponential, uniform and scalefree networks: A simple model for biodiversity collapse in foodwebs
• Studies in the physics of evolution: creation, formation, destruction
• Eigenmode of Decision-By-Majority Process on Complex Networks