Impact of intra and inter-cluster coupling balance on the performance of nonlinear networked systems

•We exploit two metrics that can capture the effects of the differences among within and between cluster couplings. These two metrics describe the energy that a system consumes to get back to the stable state and the states variation, and they are obtained in terms of irreducible representation theory.•We use the two performance metrics to investigate two paradigmatic dynamical systems, using both synthetic and real-world networks.•Our results show that for both metrics, the systems could exhibit nontrivial behavior as the balance between intra- and inter-coupling strengths is varied. The dynamical and structural aspects of cluster synchronization (CS) in complex systems have been intensively investigated in recent years. Here, we study CS of dynamical systems with intra- and inter-cluster couplings. We exploit new metrics that describe the performance of such systems and evaluate them as a function of the strength of the couplings within and between clusters. We obtain analytical results that indicate that spectral differences between the Laplacian matrices associated with the partition between intra- and inter-couplings directly affect the metrics of system performance. Our results show that the dynamics of the system might exhibit an optimal balance that optimizes its performance. Our work provides new insights into the way specific symmetry properties relate to collective behavior, and could lead to new forms to increase the controllability of complex systems and to optimize their stability.