Influence of stochastic perturbations on the cluster explosive synchronization of second-order Kuramoto oscillators on networks

Explosive synchronization in networked second-order Kuramoto oscillators has been well studied recently and it is revealed that the synchronization process is featured by cluster explosive synchronization. However, little attention has been paid to the influence of noise or perturbation. We here study this problem and discuss the influences of noise and perturbation. For the former, we interestingly find that noise has significant influence on the cluster explosive synchronization of those nodes with smaller degrees, i.e., their synchronization will change from the first-order to second-order transition and the critical points for both the forward and backward synchronization depend on the strength of noise. Especially, when the strength of noise is in an optimal range, a synchronization of the nodes with smaller degrees will be induced in the region of coupling strength where they do not display synchronization in the absence of noise. For the latter, we find that the effect of perturbation is similar to that of noise when its duration W is small. However, the perturbation will induce a change from cluster explosive synchronization to explosive synchronization when W is large. Furthermore, a brief theory is provided to explain the influence of perturbations on the critical points.