对次近邻单向耦合振子的同步研究

【目的】在Kuramoto局域耦合振子平均场模型基础上,探讨在非对称耦合作用下一维闭合环上次近邻Kuramoto相振子的同步动力学行为。【方法】在最近邻单向耦合振子的动力学模型的基础上,建立次近邻单向耦合振子的动力学模型来研究少数耦合极限环系统的行为;通过数值模拟,得出平均频率、系统序参量与耦合强度的关系;通过理论分析少体系统的动力学稳定性。【结果】通过比较文献,证明次近邻单向耦合振子对同步存在影响。当在少数耦合极限环系统下(N≤6),耦合强度大于一定阈值时,所有振子都被同步到平均频率上,序参量随耦合强度的增加而趋于1,而在振子较多(N6)时,在系统同步区域的序参量会出现多定态分支。【结论】一维闭合环上考虑次近邻耦合振子在非对称耦合作用下同步区域呈现多同步定态。非零稳态出现分支现象与耦合振子系统大小有关。

Study on Synchronization of Next-Nearest-Neighbor Oscillators with Unidirectional Coupling

Objective]Based on the mean-field Kuramoto model with local coupling,the dynamics of synchronization in one-dimensional closed ring considering the next-nearest neighbor unidirectional coupling oscillators were investigated.Methods]On the basis of the Kuramoto model with the nearest neighbor coupling,the next-nearest neighbor coupling ring was established to study the dynamic behavior of a coupling limit cycle system.The relationship of the average frequency and order parameter of the coupling strength were obtained by numerical simulation for synchronous branch of the steady states.The validity of the numerical simulation results was verified by theoretical analysis of few-body system''s dynamic stability.Results]By comparing to literatures,it proved that the next-nearest neighbor Kuramoto phase oscillators with unidirectional coupling in a ring influenced the system''s synchronization.All oscillators were synchronized to the average frequency and order parameter tended to 1 as the coupling strength was greater than a certain threshold value when the number of coupling limit cycle in few-body system was smaller than 6.While there were more coupling limit cycle in the system(N>6),the order parameter showed multi-steady branches in the synchronization region.Conclusion]The multiple stable states of synchronization are emerged under the action of the asymmetric coupling in one-dimensional closed ring with the next-nearest neighbor unidirectional coupling.Non-zero steady state occurring branches is related to the size of coupling oscillator system.