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 strong beliefs emerge on the network 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种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、内部偏见以及社会心理学最新理论中提出的多种认知失调源的影响。我们证明了网络中强信念的产生源于分岔现象，并分析了社交网络效应平衡如何控制分岔性质，进而影响信念形成的极限集解。分析提供了关于多稳态网络信念均衡及信念振荡如何依赖于通信网络图和信念系统网络图的可构造条件。本文模型与分析为社交系统动力学提供了新的理论见解，并为在存在选项间结构化关系的工程化网络上设计去中心化决策提供了新的原则性框架。