Bipartite Containment Fluctuation Behaviors of Cooperative–Antagonistic Networks With Time-Varying Topologies

This article is concerned with how the effect of time-varying topologies is overcome and the behaviors of cooperative–antagonistic networks (CANs) are identified. An extended leader–follower (ELF) framework is established for CANs, in which each leader is allowed to evolve dynamically due to the communication with its neighbor leaders. It is shown that a new class of bipartite containment fluctuation behaviors emerges in the presence of the ELF framework, regardless of any structure conditions for CANs. In particular, the leaders are clustered into separate groups, each of which can realize the modulus consensus, whereas the followers may not be enabled to converge but fluctuate within the bounded region spanned by all leaders’ states and their symmetric states. A simulation example is provided to demonstrate the effectiveness of the behavior analysis results developed for CANs.