Bipartite Consensus Control for Coupled Harmonic Oscillators Under a Coopetitive Network Topology

By extending the definition of bipartite consensus to coupled harmonic oscillators, in this paper, we investigate the problem of the bipartite consensus control of coupled harmonic oscillators in directed network topology in which positive and negative interaction weights coexist, and a distributed bipartite consensus control protocol is proposed. Based on the specific structure of the coopetitive network topology, criteria that guarantee the achievement of bipartite consensus for coupled harmonic oscillators are presented. Furthermore, the final convergent states of the oscillators are also given in terms of the initial values of the agents and a specific eigenvector of the Laplacian matrix corresponding to the coopetitive network topology. Finally, simulations are presented to validate the theoretical analysis.