多重耦合振子系统的同步动力学  

Synchronization in coupled oscillators with multiplex interactions

作　　者：王学彬 徐灿 郑志刚 Wang Xue-Bin;Xu Can;Zheng Zhi-Gang(Institute of Systems Science,Huaqiao University,Xiamen 361021,China;College of Information Science and Engineering,Huaqiao University,Xiamen 361021,China)

机构地区：[1]华侨大学系统科学研究所,厦门361021 [2]华侨大学信息科学与工程学院,厦门361021

出　　处：《物理学报》2020年第17期31-42,共12页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11875135,11905068,11847013);泉州市科技计划项目(批准号:2018C085R);华侨大学研究生科研创新基金资助的课题.

摘　　要：耦合相振子的同步研究对理解复杂系统自组织协同的涌现具有重要的理论意义.相比于传统耦合振子的两体成对耦合,多重耦合近年来得到广泛的关注.当相振子间的多重耦合机制起主要作用时,系统会涌现一系列去同步突变,这一新颖的动力学特性对理解复杂系统群体动力学提供了重要的理论启示.本文研究了平均场的三重耦合Kuramoto系统的同步动力学,发现了去同步转变具有不可逆性,并利用平均场自洽方法和无序态线性稳定性分析揭示了不可逆去同步突变的动力学机制.进一步研究发现,随着振子自然频率分布半宽度的变化,系统会经历一系列去同步驻波态的转变.在相变临界点,系统在高维相空间会通过鞍结分岔导致同步态失稳而塌缩至稳定的低维不变环面.本文的研究揭示了多重耦合函数作用的振子系统的各种协同态及其相变机制,同时可为理解其他复杂系统(如超网络结构)协同态的动力学转变提供理论借鉴.The study of synchronizations in coupled oscillators is very important for understanding the occurrence of self-organized behaviors in complex systems.In the traditional Kuramoto model that has been extensively applied to the study of synchronous dynamics of coupled oscillators,the interaction function among oscillators is pairwise.The multiplex interaction mechanism that describes triple or multiple coupling functions has been a research focus in recent years.When the multiplex coupling dominates the interactions among oscillators,the phase oscillator systems can exhibit the typical abrupt desynchronization transitions.In this paper,we extensively investigate the synchronous dynamics of the Kuramoto model with mean-field triple couplings.We find that the abrupt desynchronization transition is irreversible,i.e.the system may experience a discontinuous transition from coherent state to incoherent state as the coupling strength deceases adiabatically,while the reversed transition cannot occur by adiabatically increasing the coupling.Moreover,the coherent state strongly depends on initial conditions.The dynamical mechanism of this irreversibility is theoretically studied by using the self-consistency approach.The neutral stability of ordered state is also explained through analyzing the linear-stability of the incoherent state.Further studies indicate that the system may experience a cascade of desynchronized standing-wave transitions when the width of the distribution function of natural frequencies of oscillators is changed.At the critical coupling,the motion of coupled oscillators in high-dimensional phase space becomes unstable through the saddle-node bifurcation and collapses into a stable low-dimensional invariant torus,which corresponds to the standing-wave state.The above conclusions and analyses are further extended to the case of multi-peak natural-frequency distributions.The results in this work reveal various collective synchronous states and the mechanism of the transitions among these macroscopic state

关 键 词：同步 多重耦合 爆炸性去同步 去同步驻波态 

分 类 号：N941.4[自然科学总论—系统科学]