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Mechanism of bursting oscillations in non-smooth generalized Chua’s circuit with two time scales

Li Xu Zhang Zheng-Di Bi Qin-Sheng

Mechanism of bursting oscillations in non-smooth generalized Chua’s circuit with two time scales

Li Xu, Zhang Zheng-Di, Bi Qin-Sheng
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Publishing process
  • Received Date:  24 July 2013
  • Accepted Date:  19 August 2013
  • Published Online:  05 November 2013

Mechanism of bursting oscillations in non-smooth generalized Chua’s circuit with two time scales

  • 1. Facuity of Science, Jiangsu University, Zhenjiang 212013, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11272135, 21276115).

Abstract: By introducing periodically alternate current source as well as suitable values for the parameters to ensure that there exists order gap between the natural frequency and the exited frequency, a two-time scale namely, a fast-slow coupled non-smooth generalized Chua’s circuit model is established. Based on the corresponding generalized autonomous system, the stabilities of the equilibrium points in different regions are investigated, from which the critical conditions related to different types of bifurcation forms are obtained. At the same time, combining the theory of Clarke derivative, different types of non-conventional bifurcation models which may occur when the trajectory passes across the non-smooth boundaries are explored. Furthermore, with the combination of the generalized phase portraits, two typical periodic bursting phenomena namely, the Fold/Fold and Fold/Hopf periodic bursters, and their associated bifurcation mechanisms are analysed in detail.

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