This article focuses on solving disagreement behavior analysis problems for cooperative-antagonistic networks (CANs) subject to switching topologies, for which the extended structural balance theory is developed by concerning the local nodes instead of global CANs. A notion of simultaneously structurally balanced nodes is proposed, which helps get a role identification framework of all nodes by integrating a generalized leader–follower structure for CANs. It is shown that for any switching CANs, the behavior analysis can be performed by identifying the roles of nodes, where the disagreement behaviors are caused because of the existence of different roles of nodes. A specific class of quasi-interval bipartite consensus behaviors is characterized for CANs by the equivalence between the impact index and the number of simultaneously structurally balanced nodes. In particular, the behavior analysis results for CANs can be applied to analyze the dynamic behaviors for cooperative networks despite any switching topologies. Two simulation examples are presented to illustrate the disagreement behavior results for CANs with switching topologies.

中文翻译：

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具有拮抗作用的交换网络的扩展结构平衡和分歧行为

本文着重于解决具有交换拓扑的协作对抗网络（CAN）的不一致行为分析问题，为此，扩展关注结构平衡的理论是通过关注局部节点而不是全局CAN来开发的。提出了一种结构上同时平衡的节点的概念，该概念通过集成用于CAN的通用领导者-从属结构来帮助获得所有节点的角色识别框架。结果表明，对于任何交换式CAN，可以通过识别节点的角色来执行行为分析，其中节点行为的存在是由于节点角色不同而引起的。针对CAN，通过冲击指数与同时结构平衡的节点数之间的等效性来表征一类特定的准间隔二分共识行为。特别是，CAN的行为分析结果可用于分析协作网络的动态行为，而不考虑任何交换拓扑。给出两个仿真示例，以说明具有开关拓扑结构的CAN的不一致行为结果。