The nonlinear response of neuron firing under external electromagnetic radiation as well as transmembrane current, as two kinds of external forces, are studied in an improved Fitzhugh–Nagumo (FHN) model. The control effects of external forces to neuron firing are measured by winding number [Formula: see text] during mode transition of motion types. The phenomenon of match and mismatch between the angular frequency [Formula: see text] and the angular frequency of external forcing can be explained by whether the winding number is [Formula: see text] or not. [Formula: see text] remains as constants like [Formula: see text], [Formula: see text] and [Formula: see text], etc. The amplitude of transmembrane current [Formula: see text] is increased so that it distributes in a stair-like structure in parameter space before the system enters chaotic state when [Formula: see text] is large enough. The scenarios of motion type switching are different between and beyond in the stairs. Besides, the occurrence and the disappearance of chaos are accompanied with the destruction of the orbit with the variation of parameters which temporarily spoils the toroidal topology and induces chaotic oscillation. Indeed, nonlinear response to external forces is pivotal to neuron firing and its control.

中文翻译：

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单个神经元对外部电磁辐射的阶梯状频率响应和混沌行为的发生

在改进的 Fitzhugh-Nagumo (FHN) 模型中研究了作为两种外力的外部电磁辐射和跨膜电流下神经元放电的非线性响应。外力对神经元放电的控制作用是通过运动类型模式转换过程中的绕组数[公式：见正文]来衡量的。角频率[公式：见正文]与外力角频率的匹配和不匹配现象可以用绕组数是否为[公式：见正文]来解释。[公式：见文]保持为常数，如[公式：见文]，[公式：见文]和[公式：见文]等。跨膜电流的幅度[公式：当[公式：见文本]足够大时，在系统进入混沌状态之前，它在参数空间中呈阶梯状分布。运动类型切换的场景在楼梯之间和楼梯之外是不同的。此外，混沌的发生和消失伴随着参数变化对轨道的破坏，暂时破坏了环形拓扑结构，诱发了混沌振荡。事实上，对外力的非线性响应对于神经元放电及其控制至关重要。混沌的发生和消失伴随着参数变化对轨道的破坏，暂时破坏了环形拓扑结构，诱发了混沌振荡。事实上，对外力的非线性响应对于神经元放电及其控制至关重要。混沌的发生和消失伴随着参数变化对轨道的破坏，暂时破坏了环形拓扑结构，诱发了混沌振荡。事实上，对外力的非线性响应对于神经元放电及其控制至关重要。