Agreements of Nonlinear Opinion Dynamics in Switching Social Networks

This article formulates and analyzes agreements of the nonlinear opinion dynamics in social networks according to switching interactions, where the agents' susceptibilities depend on current states. These switching interactions are formulated by switching directed graphs with some mild joint connectivity, and depicted by nonlinear switching model. An extended LaSalle invariance principle is established for analyzing the agreements of this switching model as well as three specialized scenarios, where the limiting equations formed by the weak* convergence are used to study the steady-state behavior so that the stability analysis is substantially simplified in the sense that the “<inline-formula><tex-math notation="LaTeX">$\max - \min$</tex-math></inline-formula>” Lyapunov function may be assumed to be constant along any bounded forward complete solutions of limiting equations. Examples and simulations are used to verify the obtained results.