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Mean-Field Analysis of the q-Voter Model on Networks |
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| Authors: | Paolo Moretti Suyu Liu Claudio Castellano Romualdo Pastor-Satorras |
| Affiliation: | 1. Departamento de Electromagnetismo y Física de la Materia and Instituto “Carlos I” de Física Teórica y Computacional, Facultad de Ciencias, Universidad de Granada, Fuentenueva s/n, 18071, Granada, Spain 2. State Key Laboratory of Industrial Control Technology Institute of Cyber-System and Control, Zhejiang University, Hangzhou, 310027, P.R. China 3. Istituto dei Sistemi Complessi (ISC-CNR), via dei Taurini 19, 00185, Rome, Italy 4. Dipartimento di Fisica, “Sapienza” Università di Roma, P.le A. Moro 2, 00185, Rome, Italy 5. Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034, Barcelona, Spain |
| Abstract: | We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations. |
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