复杂系统同步的自组织动力学与统计物理学

Self-organization dynamics and statistical physics of synchronization in complex systems

构建了复杂系统自组织同步行为的一般性序参量理论;讨论了利用Ott-Antonsen拟设等降维方法得到序参量的低维动力学方程,并从微观到宏观的不同层次介绍了复杂系统同步行为的机制、形式以及各种不同表现;探讨了异质耦合振子系统的同步序参量动力学,发现了异质耦合可以导致Bellerophon态.对于高阶网络耦合振子体系,通过研究,发现了突变性的去同步转变,该转变具有不可逆性;探讨了非线性序参量耦合振子系统的同步动力学以及同步附近各种类型的相变及相应序参量的标度性质;确定了集体动力学的突然去同步过渡、连续过渡和混合过渡等3种类型的相变.这些研究对于复杂系统集体行为的深入理解和应用有重要意义.

Order-parameter theory of self-organized synchronization in complex systems is proposed.Low-dimensional dynamical equations of order parameters are derived in terms of dimension reduction schemes such as Ott-Antonsen ansatz.The mechanisms,forms,and manifestations of the emergence of synchronization are explored at both microscopic and macroscopic levels.Order parameter dynamics of synchronization in heterogeneously coupled oscillators are investigated.It is found that coupling heterogeneity may induce the Bellerophon state.Explosive desynchronization transitions are revealed in coupled oscillators with multiplex network topologies,and these transitions are irreversible.Synchronization dynamics is studied for oscillators with nonlinear couplings.Various transitions and scaling relations are investigated at the onset of synchronization.Three types of transitions(explosive,continuous and hybrid synchronizations)are identified.These studies shed light on both theoretical understandings and potential applications of collective behaviors in complex systems.