Suppressing explosive synchronization by contrarians

Explosive synchronization (ES) has recently received increasing attention and studies have mainly focused on the conditions of its onset so far. However, its inverse problem, i.e. the suppression of ES, has not been systematically studied so far. As ES is usually considered to be harmful in certain circumstances such as the cascading failure of power grids and epileptic seizure, etc., its suppression is definitely important and deserves to be studied. We here study this inverse problem by presenting an efficient approach to suppress ES from a first-order to second-order transition, without changing the intrinsic network structure. We find that ES can be suppressed by only changing a small fraction of oscillators into contrarians with negative couplings and the critical fraction for the transition from the first order to the second order increases with both the network size and the average degree. A brief theory is presented to explain the underlying mechanism. This finding underlines the importance of our method to improve the understanding of neural interactions underlying cognitive processes.