Minimum control of cluster synchronization effort in diffusion coupled nonlinear networks

This paper studies the design of minimal control effort for cluster synchronization (CS) in a diffusion-coupled nonlinear network under directed graph. Under the conditions that the directed graph satisfies the cluster input equivalence condition and the system possesses a bounded Jacobian matrix, we obtain CS of diffusion-coupled nonlinear network with non-diagonal coupling matrix. Based on matrix measure and balancing theorem, we obtain the local minimization controllers for the minimal control effort of CS. Finally, the theoretical results are validated through a numerical example involving a network of coupled FitzHugh–Nagumo neurons with a general topology of interactions.