  We introduce and analyze a continuous time and state-space model of opinion
cascades on networks of large numbers of agents that form opinions about two or
more options. By leveraging our recent results on the emergence of agreement
and disagreement states, we introduce novel tools to analyze and control
agreement and disagreement opinion cascades. New notions of agreement and
disagreement centrality, which depend only on network structure, are shown to
be key to characterizing the nonlinear behavior of agreement and disagreement
opinion formation and cascades. Our results are relevant for the analysis and
control of opinion cascades in real-world networks, including biological,
social and artificial networks, and for the design of opinion-forming behaviors
in robotic swarms. We illustrate an application of our model to a multi-robot
task-allocation problem and discuss extensions and future directions opened by
our modeling framework.
