Nonlinear Dynamics

, Volume 70, Issue 3, pp 2003–2013 | Cite as

Complex dynamics of compound bursting with burst episode composed of different bursts

  • Zhuoqin Yang
  • Qingyun WangEmail author
  • Marius-F. Danca
  • Jiaoying Zhang
Original Paper


Episodic or compound bursting arises from a transition between a burst episode composed of a long burst and several short bursts and a relatively long subthreshold oscillation in this work. The minimal and generic phantom bursting model proposed by Bertram et al. is employed to produce compound bursting of a single pancreatic β-cell and compound bursting synchronization with antiphase spikes of two electrical coupling pancreatic β-cells. Two different fast/slow analysis for the moderate and the slower slow variables in three-dimensional spaces are combined to highlight better how these two slow variables with different time scales commonly or separately result in complex dynamic of the compound bursting of both the single β-cell and the two electrical coupling β-cells. For the compound bursting synchronization with antiphase spikes, we reveal how varying coupling strength leads to a change of the number of short bursts within the burst episode for different types of compound bursting.


Compound bursting Slow variables with different time scales Electrical coupling Synchronization Fast/slow analysis 



This work is supported by the National Natural Science Foundation of China (Nos. 11072013 and 11172017).


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Zhuoqin Yang
    • 1
  • Qingyun Wang
    • 2
    Email author
  • Marius-F. Danca
    • 3
    • 4
  • Jiaoying Zhang
    • 1
  1. 1.School of Mathematics and System SciencesBeihang UniversityBeijingChina
  2. 2.Department of Dynamics and ControlBeihang UniversityBeijingChina
  3. 3.Department of Mathematics and Computer ScienceAvram Iancu UniversityCluj-NapocaRomania
  4. 4.Romanian Institute of Science and TechnologyCluj-NapocaRomania

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