Stair-Like Frequency Response of Single Neuron to External Electromagnetic Radiation and Onset of Chaotic Behaviors

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.