中国物理B ›› 2021, Vol. 30 ›› Issue (10): 100504-100504.doi: 10.1088/1674-1056/abf101

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Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points

Wen Sun(孙文)1,†, Biwen Li(李必文)1, Wanli Guo(郭万里)2, Zhigang Zheng(郑志刚)3, and Shihua Chen(陈士华)4   

  1. 1 School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China;
    2 School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China;
    3 College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China;
    4 College of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2021-01-20 修回日期:2021-02-26 接受日期:2021-03-23 出版日期:2021-09-17 发布日期:2021-09-17
  • 通讯作者: Wen Sun E-mail:sunwen_2201@163.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11875135) and Fundamental Research Funds for National University, China University of Geosciences (Wuhan) (Grant No. CUGGC05).

Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points

Wen Sun(孙文)1,†, Biwen Li(李必文)1, Wanli Guo(郭万里)2, Zhigang Zheng(郑志刚)3, and Shihua Chen(陈士华)4   

  1. 1 School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China;
    2 School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China;
    3 College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China;
    4 College of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2021-01-20 Revised:2021-02-26 Accepted:2021-03-23 Online:2021-09-17 Published:2021-09-17
  • Contact: Wen Sun E-mail:sunwen_2201@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11875135) and Fundamental Research Funds for National University, China University of Geosciences (Wuhan) (Grant No. CUGGC05).

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摘要： The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively. However, the coupled oscillators in practice are nonidentical, and there exist mismatched parameters. It has been proved that under certain conditions, complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points, yet other cooperative behaviors are not addressed. In this paper, we further consider two coupled nonidentical oscillators with the same equilibrium points, where one oscillator is convergent while the other is chaotic, and explore their cooperative behaviors. We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings. In the case of directed coupling, death islands appear in two-parameter spaces. The mechanism inducing these transitions is presented.

关键词: amplitude death, bounded chaotic synchronization, mismatched parameter

Abstract: The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively. However, the coupled oscillators in practice are nonidentical, and there exist mismatched parameters. It has been proved that under certain conditions, complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points, yet other cooperative behaviors are not addressed. In this paper, we further consider two coupled nonidentical oscillators with the same equilibrium points, where one oscillator is convergent while the other is chaotic, and explore their cooperative behaviors. We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings. In the case of directed coupling, death islands appear in two-parameter spaces. The mechanism inducing these transitions is presented.

Key words: amplitude death, bounded chaotic synchronization, mismatched parameter

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Gg (Control of chaos, applications of chaos)