The movement of large amounts of ions (e.g., potassium, sodium and calcium) in the nervous system triggers time-varying electromagnetic fields that further regulate the firing activity of neurons. Accordingly, the discharge states of a modified Hindmarsh–Rose (HR) neuron model under an electric field are studied by numerical simulation. By using the Matcont software package and its programming, the global basins of attraction for the model are analyzed, and it is found that the model has a coexistence oscillation pattern and hidden discharge behavior caused by subcritical Hopf bifurcation. Furthermore, the model’s unstable branches are effectively controlled based on the Washout controller and eliminating the hidden discharge states. Interestingly, by analyzing the two-parametric bifurcation analysis, we also find that the model generally has a comb-shaped chaotic structure and a periodic-adding bifurcation pattern. Additionally, considering that the electric field is inevitably disturbed periodically, the discharge states of this model are more complex and have abundant coexisting oscillation modes. The research results will provide a useful reference for understanding the complex dynamic characteristics of neurons under an electric field.

中文翻译：

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电场下HR神经元模型的动态表达

神经系统中大量离子（例如钾、钠和钙）的运动会触发随时间变化的电磁场，从而进一步调节神经元的放电活动。因此，通过数值模拟研究了修改后的 Hindmarsh-Rose (HR) 神经元模型在电场下的放电状态。通过使用Matcont软件包及其编程，对模型的全局吸引力盆地进行分析，发现模型具有共存振荡模式和亚临界Hopf分岔引起的隐藏放电行为。此外，基于Washout控制器有效地控制了模型的不稳定分支，消除了隐藏的放电状态。有趣的是，通过分析二参数分岔分析，我们还发现，该模型一般具有梳状混沌结构和周期加分岔模式。此外，考虑到电场不可避免地受到周期性扰动，该模型的放电状态更加复杂，并存在丰富的共存振荡模式。研究结果将为理解电场作用下神经元的复杂动态特性提供有益的参考。