We propose and analyze a nonlinear dynamic model of continuous-time multi-dimensional belief formation over signed social networks. Our model accounts for the effects of a structured belief system, self-appraisal, internal biases, and various sources of cognitive dissonance posited by recent theories in social psychology. We prove that agents become opinionated as a consequence of a bifurcation. We analyze how the balance of social network effects in the model controls the nature of the bifurcation and, therefore, the belief-forming limit-set solutions. Our analysis provides constructive conditions on how multi-stable network belief equilibria and belief oscillations emerging at a belief-forming bifurcation depend on the communication network graph and belief system network graph. Our model and analysis provide new theoretical insights on the dynamics of social systems and a new principled framework for designing decentralized decision-making on engineered networks in the presence of structured relationships among alternatives.

翻译：我们提出并分析了一个在符号社交网络上连续时间多维信念形成的非线性动态模型。该模型考虑了结构化信念系统、自我评价、内在偏见以及社会心理学近期理论提出的多种认知失调源的影响。我们证明，智能体因分岔过程而形成鲜明观点。我们分析了模型中社交网络效应的平衡如何控制分岔的性质，从而决定信念形成的极限集解。我们的分析为多稳态网络信念均衡和信念形成分岔处涌现的信念振荡如何依赖于通信网络图与信念系统网络图提供了构造性条件。该模型与分析为社会系统动力学提供了新的理论见解，并为在备选方案存在结构化关系的工程网络上设计分布式决策提供了新的原则性框架。