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时变耦合作用下一类离散Winfree模型的同步性分析

周一公, 葛斌, 高珊珊   

  1. 哈尔滨工程大学数学科学学院, 哈尔滨 150001
  • 收稿日期:2021-12-11 修回日期:2022-03-11 发布日期:2022-08-31
  • 通讯作者: 葛斌,Email:gebin791025@hrbeu.edu.cn.
  • 基金资助:
    国家自然科学基金(11201095)和中央高校基本科研业务费(3072022TS2402)资助课题.

周一公, 葛斌, 高珊珊. 时变耦合作用下一类离散Winfree模型的同步性分析[J]. 系统科学与数学, 2022, 42(7): 1660-1684.

ZHOU Yigong, GE Bin, GAO Shanshan. Synchronization Analysis of a Class of Discrete Winfree Models with Time-Varying Coupling[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(7): 1660-1684.

Synchronization Analysis of a Class of Discrete Winfree Models with Time-Varying Coupling

ZHOU Yigong, GE Bin, GAO Shanshan   

  1. College of Mathematical Sciences, Harbin Engineering University, Harbin 150001
  • Received:2021-12-11 Revised:2022-03-11 Published:2022-08-31
文章研究了一类耦合强度随时间呈周期性变化的Winfree模型.在适当的假设条件下,证明了振子的最大相位差是随耦合强度系数$K$的变化周期为时间间隔在不断减小,进而给出了该系统在一定条件下发生相位同步行为的充分条件.最后,给出了两组具体的振子耦合作用方式,并通过数值仿真实验验证了理论结果的正确性.
In this paper, we study a kind of Winfree model in which the coupling strength changes periodically with time. Under suitable assumptions, we prove that the maximum phase difference of the oscillator decreases with the change period of the coupling strength coefficient K. Furthermore, we give the sufficient condition to guarantee phase synchronization in Discrete Winfree model. Finally, we start to give two coupling modes of the oscillator, and the correctness of the theoretical analysis was verified by numerical experiments.

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