Initial-induced coexisting and synchronous firing activities in memristor synapse-coupled Morris–Lecar bi-neuron network

  • Bocheng Bao
  • Qinfeng Yang
  • Dong Zhu
  • Yunzhen Zhang
  • Quan Xu
  • Mo ChenEmail author
Original paper


A memristor synapse with threshold memductance is employed to couple two neurons for representation of the electromagnetic induction effect triggered by their membrane potential difference. This paper presents a memristor synapse-coupled bi-neuron network by bidirectionally coupling two three-dimensional heterogeneous or homogeneous Morris–Lecar neurons with such a memristor synapse. The memristive bi-neuron network possesses a line equilibrium set with its stability related to the induction coefficient and memristor initial value. Coexisting firing activities in the heterogeneous memristive bi-neuron network are explored using bifurcation plots, phase plots, and time sequences, upon which the initial-induced infinitely many firing patterns including hyperchaotic, chaotic, and periodic bursting and tonic-spiking patterns are disclosed, indicating the emergence of the initial-induced extreme multistability. Furthermore, synchronous firing activities in homogeneous memristive bi-neuron network are investigated using the time sequences, synchronization transition states, and mean synchronized errors. The results demonstrate that the synchronous firing activities are associated with the induction coefficient and specially associated with the initial values of memristor synapse and coupling neurons. Finally, an FPGA-based electronic bi-neuron network is designed to experimentally confirm the memristor initial-induced coexisting firing activities.


Memristor synapse Bi-neuron network Initial value Coexisting activity Synchronous activity 



This work was supported by the Grants from the National Natural Science Foundations of China under 51777016, 61801054, and 61601062, and the Natural Science Foundation of Jiangsu Province, China, under Grant No. BK20191451.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Information Science and EngineeringChangzhou UniversityChangzhouChina
  2. 2.Department of Electronic EngineeringNanjing University of Science and TechnologyNanjingChina

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