Journal of Neurodevelopmental Cognition
Quarterly Publication

Synchronization of Three All-to-All Coupled Hodgkin-Huxley Neurons under an Extremely Low-Frequency Sinusoidal External Electric Field

https://doi.org/10.48308/jncog.2026.242816.1030

Articles in Press, Accepted Manuscript
Available Online from 13 July 2026
Journal of Neurodevelopmental Cognition

Document Type : Original Article

Authors

Mahdi Gholampour 1
Esmaeil Mahdavi 2
Majid Amirzadeh 3

1 Physics group faculty of basic sciences Imam Ali University

2 Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran

3 Physics Group, Faculty of Basic Sciences, Imam Ali University, Tehran, Iran

Abstract
Due to the increasing technological exposure to extremely low-frequency (ELF) electromagnetic fields (frequencies less than 300 Hz) and the electrical excitability of neurons, we numerically investigate the impact of an ELF sinusoidal external electric field on the synchronization dynamics of a three-neuron all-to-all Hodgkin–Huxley (HH) network coupled via gap junctions with different output firing rates. Our findings show that the external field can modulate both the degree of synchrony and the firing rate of the network depending on the field frequency, amplitude, and coupling strength, resulting in regimes where synchrony is enhanced, reduced, or remains unchanged. Additionally, the external field can induce explosive synchronization transitions, and in a subset of parameter values (amplitude and frequency of the external electric field), some of these transitions are accompanied by very narrow hysteresis loops. We further demonstrate that the minimum gap-junction conductance required for full network synchrony can decrease, increase, or remain unchanged under external electric field stimulation, highlighting a highly nonlinear and parameter-sensitive interplay between field-driven forcing and intrinsic network dynamics.

Keywords

Hodgkin–Huxley neurons
synchronization
external electric field
hysteresis
  • Receive Date 07 December 2025
  • Revise Date 21 April 2026
  • Accept Date 30 May 2026

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