Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

doi:10.1088/1674-1056/24/2/020502

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
Accepted manuscript online:

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: yctcjhb@gmail.com

Cite this article:

Jiang Hai-Bo (姜海波), Zhang Li-Ping (张丽萍), Yu Jian-Jiang (于建江) Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure 2015 Chin. Phys. B 24 020502

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Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

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