Explosive Synchronization in Multilayer Networks With Inter-Layer Competition and Cooperation

In recent years, the study of explosive synchronization (ES) has been extended to multilayer networks by using different methods. In this paper, the synchronous transition of multilayer networks with inter-layer competition and inter-layer cooperation is studied, and it is found that ES occurs in both two layers when the proportion of interlayer cooperation is large enough. In addition, we study ES separately in terms of oscillator dynamics and network structures. Numerical experiments show that ES occurs independently of the natural frequency distribution. Furthermore, as the average degrees of networks increase, the critical coupling strength decreases. Finally, the robustness of the results is confirmed by changing the network topology of each layer.