Extended Structural Balance and Disagreement Behaviors for Switching Networks With Antagonistic Interactions

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.

Automated summary

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 to identify the roles of nodes. The equivalence between the impact index and the number of simultaneously structurally balanced nodes characterizes a specific class of quasi-interval bipartite consensus behaviors for CANs.