Nonlinear Dynamics

, Volume 96, Issue 4, pp 2341–2350 | Cite as

Autapse-induced firing patterns transitions in the Morris–Lecar neuron model

  • Xinlin Song
  • Hengtong Wang
  • Yong ChenEmail author
Original Paper


In 1948, Hodgkin identified three firing patterns of a single neuron in response to increasing the external DC input. In this work, we investigated the responses of a single neuron with an autapse based on a modified Morris–Lecar neuron model, which can exhibit the three types of firing patterns by changing only one parameter. An excitatory autapse was found to enhance the firing frequency, but an inhibitory autapse suppressed neuron firing. With excitatory autaptic feedback, the firing of a Class-1 neuron could be switched to that of a Class-2 neuron, and a Class-3 neuron could exhibit a Class-2 firing pattern. The sustained response frequency of the Class-2 neuron transferred from that of Class-3 is only dependent on the autaptic time delay, and the frequency decays gradually with increased the delay time.


Autapse Morris–Lecar neuron Firing pattern Time delay 



This work was supported by the National Natural Science Foundation of China with Grant No. 11675008 (YC), Grant No. 21434001 (YC) and Grant No. 11447027 (HTW). HTW acknowledges in addition supports from Natural Science Basic Research Plan in Shaanxi Province of China with Grant No. 2016JQ1037.

Compliance with ethical standards

Conflicts of interest

All the authors declare that there are no any conflict with the publication of this work.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Center of Soft Matter Physics and Its ApplicationsBeihang UniversityBeijingChina
  2. 2.School of Physics and Nuclear Energy EngineeringBeihang UniversityBeijingChina
  3. 3.School of Physics and Information TechnologyShaanxi Normal UniversityXi’anChina

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