TY - JOUR
T1 - Unanimity rule on networks
AU - Lambiotte, R.
AU - Thurner, S.
AU - Hanel, R.
N1 - Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2007/10/2
Y1 - 2007/10/2
N2 - We present a model for innovation, evolution, and opinion dynamics whose spreading is dictated by a unanimity rule. The underlying structure is a directed network, the state of a node is either activated or inactivated. An inactivated node will change only if all of its incoming links come from nodes that are activated, while an activated node will remain activated forever. 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 necessary for the whole system to get 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 and small world are studied in detail. Applications for food-chain dynamics and viral marketing are discussed.
AB - We present a model for innovation, evolution, and opinion dynamics whose spreading is dictated by a unanimity rule. The underlying structure is a directed network, the state of a node is either activated or inactivated. An inactivated node will change only if all of its incoming links come from nodes that are activated, while an activated node will remain activated forever. 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 necessary for the whole system to get 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 and small world are studied in detail. Applications for food-chain dynamics and viral marketing are discussed.
UR - http://www.scopus.com/inward/record.url?scp=35248870149&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.76.046101
DO - 10.1103/PhysRevE.76.046101
M3 - Article
AN - SCOPUS:35248870149
SN - 1539-3755
VL - 76
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 4
ER -