Aging in global networks with competing attractive—Repulsive interaction

Abstract

We study the dynamical inactivity of the global network of identical oscillators in the presence of mixed attractive and repulsive coupling. We consider that the oscillators are a priori in all to all attractive coupling and then upon increasing the number of oscillators interacting via repulsive interaction, the whole network attains a steady state at a critical fraction of repulsive nodes, pc. The macroscopic inactivity of the network is found to follow a typical aging transition due to competition between attractive–repulsive interactions. The analytical expression connecting the coupling strength and pc is deduced and corroborated with numerical outcomes. We also study the influence of asymmetry in the attractive–repulsive interaction, which leads to symmetry breaking. We detect chimera-like and mixed states for a certain ratio of coupling strengths. We have verified sequential and random modes to choose the repulsive nodes and found that the results are in agreement. The paradigmatic networks with diverse dynamics, viz., limit cycle (Stuart–Landau), chaos (Rössler), and bursting (Hindmarsh–Rose neuron), are analyzed.