mauch2026diffusiondriven
Diffusion-driven pattern formation in an opinion dynamical network model
The spatial organization of individuals and their interactions in communities are important factors known to preserve diversity in many complex systems. Inspired by metapopulation models from ecology, we study opinion formation using a network-based approach in which nodes represent communities of interacting agents holding one of two competing opinions, and links represent avenues of migration. Agents adapt to the dominant opinion within a community or migrate toward other communities. Using a master stability function approach, we analytically derive conditions for diffusion-driven pattern formation and identify structural features of the community network that sustain opinion diversity. Our model shows that even under minimal opinion rules, the interaction between local dynamics and community structure generates spatial patterns that allow minority opinions to persist by gaining local dominance.
Figure 1: Overview of the model. Agents hold one of two
opinions, X or Y, and populate nodes of a complex network
that are coupled by diffusion. Opinion formation on each
node is governed by two processes: (I) spontaneous flipping
of opinions and (II) opinion adjustment through the influence
of others.