  For a group of autonomous communicating agents, the ability to distinguish a
meaningful input from disturbance, and come to collective agreement or
disagreement in response to that input, is paramount for carrying out
coordinated objectives. In this work we study how a cascade of opinion
formation spreads 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 show how the triggering of an
opinion cascade and the collective decision itself depend on both the
distributed input and the node agreement and disagreement centrality,
determined by the spectral properties of the network graph. We further show how
the attention dynamics introduce an implicit threshold that distinguishes
between distributed inputs that trigger cascades and ones that are rejected as
disturbance.
