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Consensus and clustering in opinion formation on networks. (English) Zbl 1402.91617
Summary: Ideas that challenge the status quo either evaporate or dominate. The study of opinion dynamics in the socio-physics literature treats space as uniform and considers individuals in an isolated community, using ordinary differential equation (ODE) models. We extend these ODE models to include multiple communities and their interactions. These extended ODE models can be thought of as being ODEs on directed graphs. We study in detail these models to determine conditions under which there will be consensus and pluralism within the system. Most of the consensus/pluralism analysis is done for the case of one and two cities. However, we numerically show for the case of a symmetric cycle graph that an elementary bifurcation analysis provides insight into the phenomena of clustering. Moreover, for the case of a cycle graph with a hub, we discuss how having a sufficient proportion of zealots in the hub leads to the entire network sharing the opinion of the zealots.
MSC:
91D30 Social networks; opinion dynamics
91D10 Models of societies, social and urban evolution
37N40 Dynamical systems in optimization and economics
34D06 Synchronization of solutions to ordinary differential equations
Software:
HomCont; MATCONT
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