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Chin. Phys. B, 2015, Vol. 24(2): 020502    DOI: 10.1088/1674-1056/24/2/020502
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Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Jiang Hai-Boa, Zhang Li-Pinga, Yu Jian-Jiangb
a School of Mathematics, Yancheng Teachers University, Yancheng 224002, China;
b School of Information Science and Technology, Yancheng Teachers University, Yancheng 224002, China
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.
Keywords:  impulsively coupled oscillators      bifurcation      periodic solutions      Floquet theory  
Received:  18 June 2014      Revised:  10 September 2014      Published:  05 February 2015
PACS:  05.45.Ac (Low-dimensional chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: 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.
Corresponding Authors:  Jiang Hai-Bo     E-mail:

Cite this article: 

Jiang Hai-Bo, Zhang Li-Ping, Yu Jian-Jiang Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure 2015 Chin. Phys. B 24 020502

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