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Bursting oscillations, bifurcation and synchronization in neuronal systems

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  • Wang, Haixia
  • Wang, Qingyun
  • Lu, Qishao

Abstract

This paper investigates bursting oscillations and related bifurcation in the modified Morris–Lecar neuron. It is shown that for some appropriate parameters, the modified Morris–Lecar neuron can exhibit two types of fast–slow bursters, that is “circle/fold cycle” bursting and “subHopf/homoclinic” bursting with class 1 and class 2 neural excitability, which have different neuro-computational properties. By means of the analysis of fast–slow dynamics and phase plane, we explore bifurcation mechanisms associated with the two types of bursters. Furthermore, the properties of some crucial bifurcation points, which can determine the type of the burster, are studied by the stability and bifurcation theory. In addition, we investigate the influence of the coupling strength on synchronization transition and the neural excitability in two electrically coupled bursters with the same bursting type. More interestingly, the multi-time-scale synchronization transition phenomenon is found as the coupling strength varies.

Suggested Citation

  • Wang, Haixia & Wang, Qingyun & Lu, Qishao, 2011. "Bursting oscillations, bifurcation and synchronization in neuronal systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 667-675.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:8:p:667-675
    DOI: 10.1016/j.chaos.2011.06.003
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    Cited by:

    1. Song, Jian & Liu, Shenquan & Wen, Qixiang, 2022. "Geometric analysis of the spontaneous electrical activity in anterior pituitary corticotrophs," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Upadhyay, Ranjit Kumar & Mondal, Argha, 2017. "Synchronization of bursting neurons with a slowly varying d. c. current," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 195-208.
    3. Zhang, Shaohua & Zhang, Hongli & Wang, Cong & Ma, Ping, 2020. "Bursting oscillations and bifurcation mechanism in a permanent magnet synchronous motor system with external load perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.
    5. Wang, Jing & Liu, Shenquan & Liu, Xuanliang, 2014. "Quantification of synchronization phenomena in two reciprocally gap-junction coupled bursting pancreatic β-cells," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 65-71.

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