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In this paper, we investigate a general nonlinear model of opinion dynamicsin which both state-dependent susceptibility to persuasion and antagonisticinteractions are considered. According to the existing literature andsocio-psychological theories, we examine three specializations ofstate-dependent susceptibility, that is, stubborn positives scenario, stubbornneutrals scenario, and stubborn extremists scenario. Interactions among agentsform a signed graph, in which positive and negative edges represent friendlyand antagonistic interactions, respectively. Based on Perron-Frobenius propertyof eventually positive matrices and LaSalle invariance principle, we conduct acomprehensive theoretical analysis of the generalized nonlinear opiniondynamics. We obtain some sufficient conditions such that the states of allagents converge into the subspace spanned by the right positive eigenvector ofan eventually positive matrix. When there exists at least one entry of theright positive eigenvector which is not equal to one, the derived results canbe used to describe different levels of an opinion. Finally, we present twoexamples to demonstrate the effectiveness of the theoretical findings.

Generalized Dynamics in Social Networks With Antagonistic Interactions