带相移的离散时间相耦合振子系统的同步  

Synchronization of discrete-time phase coupled oscillators with phase shift

作　　者：张华 肖斯斯 ZHANG Hua;XIAO Sisi(College of Science,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《重庆理工大学学报（自然科学）》2023年第1期265-272,共8页Journal of Chongqing University of Technology：Natural Science

基　　金：重庆市教委科学技术研究项目(KJQN201901122);重庆市自然科学基金面上项目(cstc2019jcyj-msxmX0020);重庆理工大学研究生教育高质量发展项目(gzlcx20222075)。

摘　　要：研究了带有相移的离散时间型Kuramoto振子系统的相位同步和频率同步问题。首先,通过分析同一时刻任意2个振子相位差的最大值趋于零所需条件,给出了该系统达到相位同步的一个充分条件。其次,在振子固有频率各异的情形下,通过设置初始时刻任意2个振子之间相位差的上限值,得到了振子相位差的一个重要有界性质并给出了振子达到频率同步的充分条件。最后用一个含有10个振子的系统进行数值仿真,结果表明:振子频率恒同时,最大相位与最小相位之差在t=20 s时可降至0.003 6;振子固有频率各异时,频率最大值与最小值之差在t=0.3 s时达到4.066×10^(-5),验证了所得理论结果的正确性。This paper mainly studies both the phase and frequency synchronization of discrete-time Kuramoto oscillators with phase shift. Firstly, a sufficient condition for achieving phase synchronization is established by analyzing the condition under which the maximum phase difference of any two oscillators at the same time tends to be zero. Secondly, when the intrinsic frequencies of the oscillators are nonidentical to each other, a useful bounded property of the phase difference is obtained and then some sufficient conditions for achieving frequency synchronization are derived by setting the upper limit of the phase difference between any two oscillators at the initial time. Finally, the numerical simulations of a system with ten oscillators further show that, when the frequencies of the oscillators are identical to each other, the difference between the maximum and the minimum phases can reduce to 0.003 6 when t=20 s, while, when the frequencies are nonidentical to each other, the difference between the maximum and the minimum frequencies of each oscillator can even reach 4.066×10^(-5) when t=0.3 s. The numerical simulations further verify the correctness of the theoretical results.

关 键 词：Kuramoto振子 频率同步 相位同步 相移 离散时间 

分 类 号：N93[自然科学总论] O231[理学—运筹学与控制论]