Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks

Different methods have been proposed in the past few years to incite explosive synchronization (ES) in Kuramoto phase oscillators. In this work, we show that the introduction of a phase shift α in interlayer coupling terms of a two-layer multiplex network of Kuramoto oscillators can also instigate ES in the layers. As α→π/2, ES emerges along with hysteresis. The width of hysteresis depends on the phase shift α, interlayer coupling strength, and natural frequency mismatch between mirror nodes. A mean-field analysis is performed to justify the numerical results. Similar to earlier works, the suppression of synchronization is accountable for the occurrence of ES. The robustness of ES against changes in network topology and natural frequency distribution is tested. Finally, taking a suggestion from the synchronized state of the multiplex networks, we extend the results to classical single networks where some specific links are assigned phase-shifted interactions.