Additional repulsion reduces the dynamical resilience in the damaged networks

In this paper, we investigate the dynamical robustness of diffusively coupled oscillatory networks under the influence of an additional repulsive link. Such a dynamical resilience property is realized through the aging process of the damaged network of active and inactive oscillators. The aging process is one type of phase transition, mainly appearing at a critical threshold of a fraction of the inactive oscillator node where the mean oscillation amplitude of the entire network suddenly vanishes. These critical fractions of the failure nodes in the network are broadly used as a measure of network resilience. Here, we analytically derived the critical fraction of the aging process in the dynamical network. We find that the addition of the repulsive link enhances the critical threshold of the aging transition of diffusively coupled oscillators, which indicated that the dynamical robustness of the coupled network decreases with the presence of the repulsive interaction. Furthermore, we investigate the dynamical robustness of the network against the number of deteriorating repulsive links. We observed that a certain percentage of the repulsive link is enabled to produce the aging process in the entire network. Finally, the effect of symmetry-breaking coupling and the targeted inactivation process on the dynamical robustness property of damaged networks were investigated. The analytically obtained results are verified numerically in the network of coupled Stuart-Landau oscillators. These findings may help us to better understand the role of the coupling mechanism on the phase transition in the damaged network.