Diffusive Influence Systems

Influence systems seek to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while Turing-complete, influence dynamics of the diffusive type is almost surely asymptotically periodic. In addition to resolving the dynamics of a widely used family of multiagent systems, we introduce a general renormalization method for the bifurcation analysis of multiagent systems.