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Chin. Phys. B, 2016, Vol. 25(7): 070501    DOI: 10.1088/1674-1056/25/7/070501
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Bursting phenomena as well as the bifurcation mechanism in a coupled BVP oscillator with periodic excitation

Xiaofang Zhang(张晓芳), Lei Wu(吴磊), Qinsheng Bi(毕勤胜)
Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
Abstract  We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system. By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency. Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples, in which different types of bursting oscillations such as subHopf/subHopf burster, subHopf/fold-cycle burster, and double-fold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states (QSs) and the repetitive spiking states (SPs) may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically.
Keywords:  coupled BVP oscillator      two timescales      bursting oscillations      bifurcation mechanism     
Received:  02 June 2015      Published:  05 July 2016
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 21276115).
Corresponding Authors:  Xiaofang Zhang     E-mail:

Cite this article: 

Xiaofang Zhang(张晓芳), Lei Wu(吴磊), Qinsheng Bi(毕勤胜) Bursting phenomena as well as the bifurcation mechanism in a coupled BVP oscillator with periodic excitation 2016 Chin. Phys. B 25 070501

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