In this letter, we propose a continuous-time dynamics for social network that represents patterns of both amity and enmity through directed signed graphs. The introduction of discrepancies between true and perceived sentiments gives rise to a non-autonomous system and distinguishes itself from the prior models. We show that for almost all initial configurations, the system will evolve into at most four factions. Under some mild assumptions on the initial conditions, structural balance with at most two factions can be achieved, which extends the previous results for symmetric or normal initial configurations without considering the effect of perceived sentiment.

中文翻译：

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论知觉下的结构平衡动力学

在这封信中，我们提出了一种社交网络的连续时间动态，该动态网络通过有向签名图表示友善和敌意的模式。真实情绪与感知情绪之间差异的引入导致了非自治系统的出现，并使其与先前的模型区分开。我们表明，对于几乎所有初始配置，系统最多将演变为四个派系。在对初始条件的一些温和假设下，最多可以实现两个派系之间的结构平衡，从而扩展了先前关于对称或正常初始配置的结果，而无需考虑感知情绪的影响。