Shahid Beheshti University Journal of Neurodevelopmental Cognition 2645-565X 6 3 2025 10 01 Synchronization of Three All-to-All Coupled Hodgkin-Huxley Neurons under an Extremely Low-Frequency Sinusoidal External Electric Field 76 92 107244 10.48308/jncog.2026.242816.1030 EN Mahdi Gholampour Physics group faculty of basic sciences Imam Ali University 0000-0002-9553-4894 Esmaeil Mahdavi Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran Majid Amirzadeh Physics Group, Faculty of Basic Sciences, Imam Ali University, Tehran, Iran Journal Article 2025 06 07 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 inv estigate 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. https://jncog.sbu.ac.ir/article_107244_acc9612d3092b5bf3c8fe8008d350a83.pdf