Diffusion-driven pattern formation in an opinion dynamical network model
1Alfred-Wegener Institute (AWI), Institute for Chemistry and Biology of the Marine Environment (ICBM), Helmholtz Institute for Functional Marine Biodiversity (HIFMB), Im Technologiepark 5, 26129 Oldenburg, Germany; Carl-von-Ossietzky University, Carl-von-Ossietzky-Straße 9-11, 26129 Oldenburg, Germany; and , Helmholtz Center for Polar and Marine Research, Am Handelshafen 12, 27570 Bremerhaven, Germany.
Abstract:
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.
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