| Abstract: |
| We study a model designed to describe the spatial spread of opinions in a population. This model is based on the Daley-Kendall model for opinion propagation.
It consists in a system a nonlinear integral equations, and shares some ressemblances with the SIR model from epidemiology, in that it treats the transmissions of the opinions similarly to those of a virus. The crucial difference is that the Daley-Kendall has a nonlinear saturation terms, that accounts for the stiffling of the opinion.
We consider the model set on graph, so that the transmission and the stiffling depend on the neighbour nodes. We study how the opinion propagates through the graph (convergence toward steady states, speed of propagation). We also show that, in some situations, the model converges toward pattern-like steady states. |
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