Opinion Dynamics with Stubborn Neutrals and Competitive Interactions

This paper investigates a general nonlinear model of opinion dynamics with stubborn neutrals and competitive interactions. Based on Perron-Frobenius property of eventually positive matrices and LaSalle invariance principle, we conduct a comprehensive theoretical analysis of the generalized nonlinear opinion dynamics. We obtain some sufficient conditions such that the states of all agents converge into the subspace spanned by the right positive eigenvector of an eventually positive matrix. Finally, a numerical example is given to illustrate obtained results.