Explosive Synchronization And Bellerephon States In Kuramoto Model

Synchronization refers to the coherent motion in a system consisting of interacting elements,which is ubiquitous in nature and human society.In the past several decades,synchronization has been extensively studied based on the Kuramoto model.It was found that in most cases the synchronization transitions turn out to be continuous,i.e.,the second-order.In 2011,it was revealed that under certain circumstance,the discontinuous,i.e.,the first-order,synchronization transition could occur in Kuramoto model.This finding rapidly becomes the hot topic which has attracted much attention.In 2016,the ECNU group reported a novel high-order coherent state,i.e.,Bellerophon state.Such a state is quantized in terms of average frequency,nonstationary,and heterogeneous.It was first observed in the frequency-weighted Kuramoto model,then in the networked conformists and contrarians.In this thesis,we investigate the explosive synchronization and B states in classical Kuramoto model and the second-order coupling Kuramoto model based on theoretical analysis and numerical simulation.The main contents include:1.We study the synchronization in classical Kuramoto model with bimodal Lorentzian distribution.We find both explosive and continuous transitions,and obtain the critical coupling strength.2.We observe B state in in classical Kuramoto model with bimodal Lorentzian distribution,showing that B state is not dependent on specific models.3.We also study the synchronization in classical Kuramoto model with bimodal triangle distribution and asymmetric bimodal Lorentzian distribution.We observe both explosive and continuous transitions,as well as B state,showing that B state is not dependent on special frequency distributions.4.We further study the clustering synchronization in second-order coupling Kuramoto model,and solve the critical point based on OA reduction method and linear stability analysis.5.We observe both explosive and continuous transitions,as well as B state in second-order coupling Kuramoto model.This work not only enhances our understanding of the collective behaviors in coupled phase oscillators,but also promotes the development of sychronization theory.