In this paper, we investigate a general nonlinear model of opinion dynamics in which both state-dependent susceptibility to persuasion and antagonistic interactions are considered. According to the existing literature and socio-psychological theories, we examine three specializations of state-dependent susceptibility, that is, stubborn positives scenario, stubborn neutrals scenario, and stubborn extremists scenario. Interactions among agents form a signed graph, in which positive and negative edges represent friendly and antagonistic interactions, respectively. We conduct a comprehensive theoretical analysis of the generalized nonlinear opinion dynamics. For stubborn positives and stubborn neutrals scenarios, the general model is well-posed if and only if the system matrix is diagonally dominant. Based on the property of limit set and the existing results, we obtain some sufficient conditions such that the states of all agents converge to specific equilibrium point or bipartite consensus. For stubborn extremists scenario, by using the Perron–Frobenius property of eventually positive matrices, we establish 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. When there exists at least one entry of the equilibrium point or right positive eigenvector which is not equal to one, the derived results can be used to describe different levels of an opinion. In addition, for stubborn extremists scenario, we also consider the cases that the system matrix forms the opposing Laplacian and repelling Laplacian matrix, respectively. Finally, we present two examples to demonstrate the effectiveness of the theoretical findings.

在本文中，我们研究了一个通用的非线性模型 of opinion dynamics in which both state-dependent susceptibility to persuasion and antagonistic interactions are considered. According to the existing literature and socio-psychological theories, we examine three specializations of state-dependent susceptibility, that is, stubborn positives scenario, stubborn neutrals scenario, and stubborn extremists scenario. Interactions among agents form a signed graph, in which positive and negative edges represent friendly and antagonistic interactions, respectively. We conduct a comprehensive theoretical analysis of the generalized nonlinear opinion dynamics. For stubborn positives and stubborn neutrals scenarios, the general model is well-posed if and only if the system matrix is diagonally dominant. Based on the property of limit set and the existing results, we obtain some sufficient conditions such that the states of all agents converge to specific equilibrium point or bipartite consensus. For stubborn extremists scenario, by using the Perron–Frobenius property of eventually positive matrices, we establish some sufficient conditions such that the states of all agents converge into the subspace由最终正矩阵的右正特征向量所覆盖。当存在至少一个不等于1的平衡点或右正特征向量项时，得出的结果可用于描述不同级别的观点。此外，对于顽固的极端主义者，我们还考虑了系统矩阵分别形成对立的拉普拉斯矩阵和排斥的拉普拉斯矩阵的情况。最后，我们提供两个例子来证明理论发现的有效性。