Bursting oscillations induced by bistable pulse-shaped explosion in a nonlinear oscillator with multiple-frequency slow excitations

  • Mengke Wei
  • Xiujing HanEmail author
  • Xiaofang Zhang
  • Qinsheng Bi
Original paper


This paper investigates bursting dynamics of a Rayleigh oscillator with multiple-frequency slow excitations, in which two different bursting patterns related to the bistable pulse-shaped explosion (PSE) are obtained. Typically, the PSE, a novel sharp transition behavior reported recently, can be observed in the Rayleigh oscillator. We show that if there is an initial phase difference \(-\frac{\pi }{2}\) between the slow excitations, two coexisting solution branches exhibiting PSE, which we call bistable PSE, may be created in the fast subsystem. Then, the route to bursting by the bistable PSE is analyzed, and two different bursting patterns, i.e., bursting of point–point type and bursting of cycle–cycle type, are obtained. Our findings show that the initial phase difference of excitations may have great effects on PSE, which thus plays an important role in transitions to different attractors and complex bursting dynamics.


Bistable pulse-shaped explosion Multiple-frequency slow excitations Initial phase difference Rayleigh oscillator Bursting oscillations 



The authors express their gratitude to the anonymous reviewers whose comments and suggestions have helped improve this paper. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11572141, 11632008, 11772161, 11872188 and 11502091), the Qing Lan Project of Jiangsu Province, the Training program for Young Talents of Jiangsu University and the Scientific Research Innovation Project for students of Jiangsu University (Grant No. 18A415).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Civil Engineering and MechanicsJiangsu UniversityZhenjiangPeople’s Republic of China

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