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Codimension-two bifurcation analysis on firing activities in Chay neuron model

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  • Duan, Lixia
  • Lu, Qishao

Abstract

Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:5:p:1172-1179
    DOI: 10.1016/j.chaos.2005.08.179
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    Cited by:

    1. Yu, Xihong & Bao, Han & Chen, Mo & Bao, Bocheng, 2023. "Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    2. 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.

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