Neural Network-based Stability Guarantee for Dissensus Opinion Behaviors on the Sphere

In this paper, we develop a neural network-based method to study opinion behaviors under a covariance-based dissensus algorithm. Driven by this dissensus algorithm, the opinions are updated based on relative interactions and gradually converge to dissensus on the sphere. This proposed neural network-based method samples data and trains a neural network to ensure the Lyapunov conditions, which significantly simplifies the Lyapunov function design for stability analysis. The regions of attraction for different dissensus equilibria can also be estimated under opinion dynamics on a unit sphere by training a neural network to approximate the solution of Zubov’s equation. Simulations demonstrate the performance of the proposed method.