Nonlinear Dynamics

, Volume 97, Issue 4, pp 2661–2673 | Cite as

Capacitor coupling induces synchronization between neural circuits

  • Zhilong Liu
  • Chunni WangEmail author
  • Wuyin Jin
  • Jun Ma
Original paper


The signal propagation and information encoding in neurons are much dependent on the activation of synapses function. Electric synapse often plays short-range modulation so that neurons can give fast responses to external stimulus while chemical synapse keeps active under long-range modulation on neural activities. Each neuron can be considered as an intelligent signal processor and appropriate setting in parameters in the electric devices can build reliable neural circuits to detect effective signal exchange and propagation. In this paper, a two-variable FitzHugh–Nagumo electrical oscillator driven by a sinusoidal voltage source is used to investigate the synchronization when the coupling capacitor is activated, which both of the plates of the coupling capacitor can trigger time-varying electric field in the capacitor, and energy flow is propagated to modulate the outputs of neural circuits. The circuit equations are obtained, and scale transformation is applied to get a dimensionless dynamical system under field coupling, and the error function for output voltage and phases is calculated to judge whether complete synchronization and phase synchronization can be realized by selecting different capacitances for the coupling capacitor. It is found that synchronization realization between neurons can be controlled by adjusting the capacitance of coupling capacitor. For two identical neurons driven by the same stimulus, complete synchronization is reached, while phase synchronization is stabilized when neurons are driven by different stimuli as the capacitor coupling is switched on. Furthermore, the realization of complete synchronization is verified on the analog circuits. It provides another new scheme for synchronization realization between neurons and a new mechanism for signal encoding in neurons via field coupling is explained.


Neural circuit Field coupling Phase synchronization Capacitor 



This project is partially supported by National Natural Science Foundation of China under Grant No.11765011, and the HongLiu first-class disciplines Development Program of Lanzhou University of Technology. The authors give great thanks to Dr. Fuqiang Wu for checking the numerical results and producing Fig. 10 in this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhysicsLanzhou University of TechnologyLanzhouChina
  2. 2.School of Mechanical and Electronical EngineeringLanzhou University of TechnologyLanzhouChina

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