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Dynamics and transitions of firing patterns in deterministic and stochastic neuronal systems

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  • Lu, Qishao
  • Yang, Zhuoqin
  • Duan, Lixia
  • Gu, Huaguang
  • Ren, Wei

Abstract

Some recent work on experimental and theoretical studies on complex firing patterns of neurons and their dynamical mechanisms is reviewed. At first, experimental results on various neural firings and the bifurcation scenarios of ISI series are discovered in neural pacemakers. Next, a thorough analysis on dynamical behaviour and transitions of neuronal firing patterns, including the period-adding bursting sequence without chaos, the integer multiple firing and GWN-induced firing activities, are demonstrated in both the deterministic and stochastic Chay neuronal systems by means of the bifurcation theory and fast/slow dynamics. Finally, the parameter regions for different types of bursting as well as their transitions in the Chay and ML neuronal systems are presented.

Suggested Citation

  • Lu, Qishao & Yang, Zhuoqin & Duan, Lixia & Gu, Huaguang & Ren, Wei, 2009. "Dynamics and transitions of firing patterns in deterministic and stochastic neuronal systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 577-597.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:577-597
    DOI: 10.1016/j.chaos.2007.08.040
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    References listed on IDEAS

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    1. Yang, Zhuoqin & Lu, Qishao & Li, Li, 2006. "The genesis of period-adding bursting without bursting-chaos in the Chay model," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 87-95.
    2. Duan, Lixia & Lu, Qishao, 2006. "Codimension-two bifurcation analysis on firing activities in Chay neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1172-1179.
    3. Yang, Zhuoqin & Lu, Qishao & Li, Li, 2006. "The genesis of period-adding bursting without bursting-chaos in the Chay model," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 689-697.
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    Cited by:

    1. Lu, Bo & Gu, Huaguang & Wang, Xianjun & Hua, Hongtao, 2021. "Paradoxical enhancement of neuronal bursting response to negative feedback of autapse and the nonlinear mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Makouo, L. & Woafo, P., 2017. "Experimental observation of bursting patterns in Van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 95-101.
    3. Xing, Miaomiao & Song, Xinlin & Wang, Hengtong & Yang, Zhuoqin & Chen, Yong, 2022. "Frequency synchronization and excitabilities of two coupled heterogeneous Morris-Lecar neurons," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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