Dynamical robustness in presence of attractive-repulsive interactions

Abstract

We investigate dynamical robustness in a network of oscillators having a simultaneous presence of attractive coupling along with a repulsive coupling. Our study reveals that the interplay of attractive-repulsive interactions in oscillators gives rise to complex aging transition dynamics. In particular, we show that due to the counteracting effects of attractive-repulsive interactions, aging transition happens through both homogeneous as well as inhomogeneous steady state. Our result establishes that while attractive interaction decreases dynamical robustness, repulsive interaction might enhance it depending on the parameter space. Parameter values for which aging transition occurs through the homogeneous steady state, dynamical robustness improves with the increment of repulsive coupling strength. For aging transition through inhomogeneous steady state phase transition is quite dramatic. It follows a discontinuous jump in the order parameter mediated by the inhomogeneous steady state. We also show that depending upon distinct coupling ranges, aging transition happens without a single inactive oscillator due to presence of inhomogneous steady state. We also study the bifurcations responsible for such complex aging transition phenomena.