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The genesis of period-adding bursting without bursting-chaos in the Chay model

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  • Yang, Zhuoqin
  • Lu, Qishao
  • Li, Li

Abstract

According to the period-adding firing patterns without chaos observed in neuronal experiments, the genesis of the period-adding “fold/homoclinic” bursting sequence without bursting-chaos is explored by numerical simulation, fast/slow dynamics and bifurcation analysis of limit cycle in the neuronal Chay model. It is found that each periodic bursting, from period-1 to period-7, is separately generated by the corresponding periodic spiking pattern through two period-doubling bifurcations, except for the period-1 bursting occurring via a Hopf bifurcation. Consequently, it can be revealed that this period-adding bursting bifurcation without chaos has a compound bifurcation structure with transitions from spiking to bursting, which is closely related to period-doubling bifurcations of periodic spiking in essence.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:1:p:87-95
    DOI: 10.1016/j.chaos.2004.12.015
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    Cited by:

    1. Han, Chunxiao & Wang, Jiang & Deng, Bin, 2009. "Fire patterns of modified HH neuron under external sinusoidal ELF stimulus," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2045-2054.
    2. Xu, Quan & Tan, Xiao & Zhu, Dong & Bao, Han & Hu, Yihua & Bao, Bocheng, 2020. "Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. 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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