Opinion Formation in a Spatially Constrained Coevolving Nonlinear Voter Model
arXiv:2607.13616
The paper studies how limiting interactions to nearby neighbors in a coevolving nonlinear voter model on random geometric graphs changes the system’s absorbing states, leading to reduced consensus, spatial fragmentation, and isolated nodes, and provides a phenomenological description of the mean‑degree evolution.
Abstract
We investigate a spatially constrained coevolving nonlinear voter model. Using a random geometric graph, we constrain the interaction range of voter dynamics. If local rewiring is not possible, the discordant link is deleted. Our results reveal absorbing states that differ not only in magnetization and activity, but also in mean degree and spatial state organization. By exploring dynamical and structural observables, we found that distinct regimes from the existing coevolving nonlinear voter model are characterized by a reduced consensus region, spatially segregated fragmentation, and isolated node formation. Additionally, we develop a phenomenological description of the evolution of the mean degree and terminal non-conserved quantities that is consistent with the numerical results. Our model highlights how local geometric accessibility reshapes the structure of the absorbing states.