平均场反馈下全局耦合Stuart-Landau极限环系统的可解集体动力学  

Solvable collective dynamics of globally coupled Stuart-Landau limit-cycle systems under mean-field feedback

作　　者：贺苏娟 邹为 He Su-Juan;Zou Wei(School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China)

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《物理学报》2023年第20期185-194,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12075089)资助的课题.

摘　　要：耦合Stuart-Landau极限环系统为研究含振幅自由度的自持续振荡系统同步相变和集体动力学提供了一个重要的范式模型.本文研究了平均场反馈下全局耦合Stuart-Landau极限环系统中3种典型的可解集体动力学:非相干态、振幅死亡及锁频态.在热力学极限N→∞情形下,利用非相干态线性稳定性分析揭示了耦合系统中同步发生的临界条件,发现了增强平均场反馈强度可使得耦合系统在更小的扩散耦合强度下出现同步相变行为;通过对振幅死亡态的线性稳定性分析得到了参数空间中振幅死亡的稳定区,发现了平均场反馈强度可有效地消除耦合系统中的振幅死亡现象;从理论上分析了锁频态的存在性条件,并从锁频态序参量的自洽关系中推导出了振幅死亡区的边界线.本文的研究揭示了平均场反馈对耦合非线性系统中集体行为的动力学控制作用,加深了平均场反馈技术对耦合诱导的集体行为影响的理解,进一步阐释了复杂耦合系统中自组织行为的涌现规律与机制.N!1 Coupled Stuart-Landau limit-cycle system serves as an important paradigmatic model for studying synchronization transitions and collective dynamics in self-sustained nonlinear systems with amplitude degree of freedom.In this paper,we extensively investigate three typical solvable collective behaviors in globally coupled Stuart-Landau limit-cycle systems under mean-field feedback:incoherence,amplitude death,and locked states.In the thermodynamic limit of N→∞,the critical condition characterizing the transition from incoherence to synchronization is explicitly obtained via performing the linear stability of the incoherent states.It is found that the synchronization transition occurs at a smaller coupling strength when the strength of mean-field feedback is gradually enhanced.The stable regions of amplitude death are theoretically obtained via an analysis of the linear stability of coupled systems around the origin.The results indicate that the existence of mean-field feedback can effectively eliminate the amplitude death phenomenon in the coupled systems;furthermore,the existence of locked states is analyzed theoretically,and in particular,the boundary of stable amplitude death region is re-derived from the self-consistent relation of the order parameter for the locked states.This work reveals the key role of mean-field feedback in controlling the collective dynamics of coupled nonlinear systems,deepens the understanding of the influence of mean-field feedback technology on the coupling-induced collective behaviors,and is conductive to our further understanding of the emerging rules and the underlying mechanisms of self-organized behavior in complex coupled systems.

关 键 词：耦合非线性振子 集体动力学 相变 振幅死亡 

分 类 号：O415[理学—理论物理]