Nonlinear Dynamics

, Volume 96, Issue 3, pp 1895–1908 | Cite as

Coherence resonance of the spiking regularity in a neuron under electromagnetic radiation

  • Juan WuEmail author
  • Shaojuan Ma
Original Paper


The electrical activities are investigated in an improved Hindmarsh–Rose (HR) model with the external electromagnetic radiation of Gaussian noise. The mode transitions of the electrical activities induced by Gaussian noise are presented, such as from the rest states to the spiking states and from the spiking states to the spiking states with more or less spikes. Then, the stationary probability distribution functions of the membrane potential of the neuronal spiking are studied to explore the effect of Gaussian noise on the strength of the spiking of the neuron for the different modes of the electrical activities. In addition, the coherence of the spiking regularity of the electrical activities is investigated. The two-dimensional and three-dimensional inverse of the normalized coefficient of the variation of the spiking regularity in the improved HR with external electromagnetic radiation as Gaussian noise and external forcing current are analyzed. Then, the coherence resonance phenomenon induced by the Gaussian noise and external forcing current is discussed under three different modes of the electrical activities. The excitable effect of Gaussian noise and external forcing current on the spiking regularity of the electrical activities is explored. It is found that Gaussian noise can induce the mode transitions of the different electrical activities of the HR neuron and improve the strength of the spiking of the neuron. Gaussian noise and external forcing current can both optimally promote the spiking regularity of the different electrical activities of the neuron.


Electrical activity Coherence resonance Random noise Electromagnetic radiation 



This work was supported by the National Natural Science Foundation of China under Grant Nos. 11602003, 11572231 and 11771018.

Compliance with ethical standards

Conflict of interest

We declare that we have no conflict of interest in the manuscript.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.China (Xi’an) Institute for Silk Road ResearchXi’an University of Finance and EconomicsXi’anChina
  2. 2.School of Mathematics & Information ScienceNorth Minzu UniversityYinchuanChina

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