基于状态转移矩阵的协作与对抗分离在意见动力学中的方法
A State Transition Matrix-Based Approach to Separation of Cooperations and Antagonisms in Opinion Dynamics
AI总结：
本文提出基于状态转移矩阵的方法，用于分析意见动力学中的协作与对抗分离，无需假设网络连通性或结构平衡性，解决收敛问题并推广结构平衡理论。
摘要：
本文关注在存在协作和对抗的情况下意见动态的演化。通过有向图的符号流类进行研究，开发了一种基于状态转移矩阵的方法，用于分析意见动态，无论网络连通性、结构平衡或有向图符号对称性。证明了基于协作与对抗的分离，可以在有向图和传统有向图下的意见动态之间建立关系，有助于解决收敛问题。特别是，二分共识（或稳定性）当且仅当相关的切换符号有向图同时结构平衡（或不平衡），从而将结构平衡理论的应用推广到变化的网络拓扑情况。
英文摘要：
This paper is concerned with the dynamics evolution of opinions in the presence of both cooperations and antagonisms. The class of Laplacian flows is addressed through signed digraphs subject to switching topologies. Further, a state transition matrix-based approach is developed for the analysis of opinion dynamics, regardless of any assumptions on connectivity, structural balance or digon sign-symmetry of signed digraphs. It is shown that based on the separation of cooperations and antagonisms, a relationship can be bridged between opinion dynamics under signed digraphs and under conventional digraphs. This helps to solve convergence problems for opinion dynamics. In particular, bipartite consensus (or stability) emerges if and only if the associated switching signed digraph is simultaneously structurally balanced (or unbalanced), which generalizes the use of structural balance theory in opinion dynamics to the case study of changing network topologies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
