Explosive synchronization in bipartite networks

Abstract

The phenomenon of explosive synchronization where asynchronous oscillators abruptly undergo synchronization in complex networks is often considered to be an emergent effect due to correlations imposed on system parameters. However, such correlation constraints avoid flexibility, generality, and applicability. We consider classical Kuramoto oscillators on complete bipartite networks with frequency heterogeneity. We observe that the presence of two different timescales between oscillators in the two partitions gives rise to explosive synchronization, first-order phase transitions, and hysteresis. Macroscopic quantitative measures like order parameter and the average phase of oscillators are derived to describe the explosive synchronization. Further, the critical points for the first-order phase transitions are obtained analytically. Finally, the analytical estimates are compared with numerical results, and they are found to be in good agreement.