›› 2015, Vol. 24 ›› Issue (2): 20502-020502.doi: 10.1088/1674-1056/24/2/020502

• GENERAL • 上一篇    下一篇

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

姜海波a, 张丽萍a, 于建江b   

  1. a School of Mathematics, Yancheng Teachers University, Yancheng 224002, China;
    b School of Information Science and Technology, Yancheng Teachers University, Yancheng 224002, China
  • 收稿日期:2014-06-18 修回日期:2014-09-10 出版日期:2015-02-05 发布日期:2015-02-05
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11402224, 11202180, 61273106, and 11171290), the Qing Lan Project of the Jiangsu Higher Educational Institutions of China, and the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and Presidents.

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Jiang Hai-Bo (姜海波)a, Zhang Li-Ping (张丽萍)a, Yu Jian-Jiang (于建江)b   

  1. a School of Mathematics, Yancheng Teachers University, Yancheng 224002, China;
    b School of Information Science and Technology, Yancheng Teachers University, Yancheng 224002, China
  • Received:2014-06-18 Revised:2014-09-10 Online:2015-02-05 Published:2015-02-05
  • Contact: Jiang Hai-Bo E-mail:yctcjhb@gmail.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11402224, 11202180, 61273106, and 11171290), the Qing Lan Project of the Jiangsu Higher Educational Institutions of China, and the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and Presidents.

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摘要： Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincaré map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincaré map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations.

关键词: impulsively coupled oscillators, bifurcation, periodic solutions, Floquet theory

Abstract: Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincaré map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincaré map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations.

Key words: impulsively coupled oscillators, bifurcation, periodic solutions, Floquet theory

中图分类号:  (Low-dimensional chaos)

  • 05.45.Ac
05.45.Pq (Numerical simulations of chaotic systems)