Explosive Synchronization With Asymmetric Frequency Distributions

Explosive synchronization refers to the discontinuous(first-order)synchronization transition with hysteresis as the coupling strength increases in coupled oscillators.It has rapidly become a hot topic in frontiers since it was discovered by a Spanish group in 2011.Later,Xin Hu and Xiyun Zhang proposed a new generalized Kuramoto model with frequency-weighted coupling and carried out a series of works based on this model.To favor the theoretical analysis,so far the frequency-weighted Kuramoto model has only been studied with symmetric frequency distributions,while the effects of the asymmetric frequency distributions are still unknown.Motivated by this,in this thesis we investigated the synchronization in such model with typical asymmetric frequency distributions.Based on numerical simulations and theoretical analysis,we found the following main results:1.Explosive synchronization can be generally observed in the frequency-weighted Kuramoto model with various asymmetric frequency distributions.As the effect of the asymmetry increases,the synchronization transition gradually converts from the first-order to the second-order;2.A novel coherent state,i.e.,the intermittent Bellerophon state,has been identified in such model with asymmetric Lorentzian distribution or asymmetric triangle distribution.These results help us obtain thorough understanding of the explosive synchronization in the frequency-weighted model.