中国物理B ›› 2018, Vol. 27 ›› Issue (11): 110501-110501.doi: 10.1088/1674-1056/27/11/110501

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇    下一篇

Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model

Ran Zhang(张冉), Miao Peng(彭淼), Zhengdi Zhang(张正娣), Qinsheng Bi(毕勤胜)   

  1. 1 Faculty of Science, Jiangsu University, Zhenjiang 212013, China;
    2 Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
  • 收稿日期:2018-05-15 修回日期:2018-07-06 出版日期:2018-11-05 发布日期:2018-11-05
  • 通讯作者: Zhengdi Zhang E-mail:747524263@qq.com
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Grant No. 11472116), the Key Program of the National Natural Science Foundation of China (Grant No. 11632008), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX17_1784).

Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model

Ran Zhang(张冉)1, Miao Peng(彭淼)1, Zhengdi Zhang(张正娣)1, Qinsheng Bi(毕勤胜)2   

  1. 1 Faculty of Science, Jiangsu University, Zhenjiang 212013, China;
    2 Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
  • Received:2018-05-15 Revised:2018-07-06 Online:2018-11-05 Published:2018-11-05
  • Contact: Zhengdi Zhang E-mail:747524263@qq.com
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Grant No. 11472116), the Key Program of the National Natural Science Foundation of China (Grant No. 11632008), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX17_1784).

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摘要：

Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamic behaviors. Due to the existence of non-smooth factors, different types of bifurcations are presented in spiking states, such as grazing-sliding bifurcation and across-sliding bifurcation. In addition, the non-smooth fold bifurcation may lead to the appearance of a special quiescent state in the interface as well as a non-smooth homoclinic bifurcation phenomenon. Due to these bifurcation behaviors, a special transition between spiking and quiescent state can also occur.

关键词: multiple time scales, grazing bifurcation, across-sliding bifurcation, non-smooth homoclinic bifurcation

Abstract:

Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamic behaviors. Due to the existence of non-smooth factors, different types of bifurcations are presented in spiking states, such as grazing-sliding bifurcation and across-sliding bifurcation. In addition, the non-smooth fold bifurcation may lead to the appearance of a special quiescent state in the interface as well as a non-smooth homoclinic bifurcation phenomenon. Due to these bifurcation behaviors, a special transition between spiking and quiescent state can also occur.

Key words: multiple time scales, grazing bifurcation, across-sliding bifurcation, non-smooth homoclinic bifurcation

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
82.40.Bj (Oscillations, chaos, and bifurcations)