Control of Agreement and Disagreement Cascades with Distributed Inputs

For a group of autonomous communicating agents to carry out coordinated objectives, it is paramount that they can distinguish meaningful input from disturbance, and come rapidly and reliably to agreement or disagreement in response to that input. We study how opinion formation cascades through a group of networked decision makers in response to a distributed input signal. Using a nonlinear opinion dynamics model with dynamic feedback modulation of an attention parameter, we prove how the triggering of an opinion cascade and the collective decision itself depend on both the distributed input and node agreement and disagreement centrality indices, determined by the spectral properties of the network graph. Moreover, we show how the attention dynamics introduce an implicit threshold that distinguishes between distributed inputs that trigger cascades and ones that are rejected as disturbance.