FitzHugh–Nagumo model

The FitzHugh - Nagumo model ( FitzHugh after Richard (* 1922) and J. Nagumo, who developed the model independently) describes a prototype of an excitable system, for example a neuron. If the external excitation exceeds a threshold, the system performs a typical excursion in - phase space before the variables and return to their rest values. This behavior is a model for the generation of spikes ( = short-term increase in membrane potential ) in a neuron after stimulation by an external current.

The equations of this dynamical system

The excitation dynamics can be represented graphically using the zero klinai. The stationary point (resting values ​​) is the intersection of the - and - zero klinai. If the system for a short time stimulated (), it describes an excursion in phase space, which can be divided into four stages: first describes the trajectory of a nearly horizontal trajectory, because due to apply. Once the trajectory reaches the cubic zero - Kline is rapidly declining, and the trajectory follows the zero klinai. At the upper apex of the zero klinai, a further horizontal passage to the left branch of the zero Kline, and then a further phase in which the trajectory of the zero klinai follows.

The FitzHugh - Nagumo model is a simplified version of the Hodgkin -Huxley model, which depicts in detail the activation and deactivation dynamics in a spiking neuron. In the original articles of FitzHugh this model is also called the Bonhoeffer- van der Pol oscillator, since it contains the van der Pol oscillator as a special case for.