Bipartite Synchronization Control for Discrete-Time Coupled Harmonic Oscillators

In this paper, we study the bipartite synchronization problem of discrete-time coupled harmonic oscillators over a coopetition network topology, and a distributed bipartite synchronization control protocol in coopetition networks is proposed. Under the directed signed network, we obtain the conditions for the designed control protocol to achieve bipartite synchronization by using algebraic graph theory and matrix theory. Through theoretical analysis, we find that the system can achieve bipartite synchronization control if the structurally balanced topology has a directed spanning tree and the sampling period satisfies certain conditions related to position gain, coupling gain and the eigenvalues of the Laplacian matrix. Finally, the effectiveness of the proposed control algorithm is verified by numerical simulation.