Semi-explosive and abrupt death via attractive-repulsive conjugate coupling

Abstract

Real-world systems often exhibit abrupt transitions due to the interplay between opposing forces. This work explores how attractive-repulsive conjugate couplings influence such explosive transitions in complex networks of nonlinear oscillators. We analyze the dynamics leading to two distinct transition types, semi-explosive and abrupt transitions, leading to amplitude death and oscillation death respectively. Our findings reveal that the transition type depends on a combination of factors: the strengths of attractive and repulsive coupling, the inherent frequency of the oscillators, and the amplitude of the oscillators. To demonstrate the generality of our observations, we present numerical results for a globally coupled network of Stuart-Landau oscillators, independent of the specific network structure. Additionally, we provide analytical verification to support our findings.