中国物理B ›› 2016, Vol. 25 ›› Issue (7): 70501-070501.doi: 10.1088/1674-1056/25/7/070501

• GENERAL • 上一篇    下一篇

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)   

  1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
  • 收稿日期:2015-06-02 出版日期:2016-07-05 发布日期:2016-07-05
  • 通讯作者: Xiaofang Zhang E-mail:xfzhang@ujs.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 21276115).

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)   

  1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
  • Received:2015-06-02 Online:2016-07-05 Published:2016-07-05
  • Contact: Xiaofang Zhang E-mail:xfzhang@ujs.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 21276115).

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摘要： 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.

关键词: coupled BVP oscillator, two timescales, bursting oscillations, bifurcation mechanism

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.

Key words: coupled BVP oscillator, two timescales, bursting oscillations, bifurcation mechanism

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Pq (Numerical simulations of chaotic systems)