I will present a model of continuous-time opinion dynamics for an arbitrary number of agents that communicate over a network and form real-valued opinions about an arbitrary number of options. The model generalizes linear and nonlinear models in the literature. Drawing from biology, physics, and social psychology, we introduce an attention parameter to modulate social influence and a saturation function to bound inter-agent and intra-agent opinion exchanges. This yields simply parameterized dynamics that exhibit the range of opinion formation behaviors predicted by model-independent bifurcation theory but not exhibited by linear models or existing nonlinear models. Behaviors include reliable formation of consensus and dissensus, even in homogeneous networks, and opinion cascades. The opinion dynamics also display ultra-sensitivity to inputs, robustness to disturbance, and flexible transitions between consensus and dissensus. Augmenting the opinion dynamics with feedback dynamics for the attention parameter results in tunable thresholds that govern sensitivity, robustness, and flexibility. The model provides new means for systematic study of dynamics on natural and engineered networks, from information spread and political polarization to collective decision making and dynamic task allocation.
This is joint work with Alessio Franci (UNAM, Mexico) and Anastasia Bizyaeva (Princeton).
Naomi Ehrich Leonard is Edwin S. Wilsey Professor of Mechanical and Aerospace Engineering and associated faculty in Applied and Computational Mathematics at Princeton University. She is a MacArthur Fellow, and Fellow of the American Academy of Arts and Sciences, SIAM, IEEE, IFAC, and ASME. She received her BSE in Mechanical Engineering from Princeton University and her PhD in Electrical Engineering from the University of Maryland. Her current research focuses on dynamics and control of multi-agent systems on networks with application to multi-robotic teams, decision making, spreading processes, and collective animal behavior.