FitzHugh–Nagumo model

The FitzHugh-Nagumo model (named after Richard FitzHugh, 1922–2007) describes a prototype of an excitable system, i.e., a neuron.

If the external stimulus $I\_\{\; m\; ext\}$ exceeds a certain threshold value, the system will exhibit a characteristic excursion in phase space, before the variables $v$ and $w$ relax back to their rest values.

This behaviour is typical for spike generations (=short elevation of membrane voltage $v$) in a neuron after stimulation by an external input current.

The equations for this dynamical system read

: $dot\{v\}=v-v^3\; -\; w\; +\; I\_\{\; m\; ext\}$

: $au\; dot\{w\}\; =\; v-a-b\; w.$

The dynamics of this system can be nicely described by zapping between the left and right branch of the cubic nullcline.

The FitzHugh-Nagumo model is a simplified version of the Hodgkin-Huxley model which models in a detailed manner activation and deactivation dynamics of a spiking neuron. In the original papers of FitzHugh this model was called Bonhoeffer-van der Pol oscillator, since it contains the van der Pol oscillator as a special case for $a=b=0$.

ee also

*Biological neuron models
*Computational neuroscience
*Hodgkin-Huxley model

References

*FitzHugh R. (1955) Mathematical models of threshold phenomena in the nerve membrane. Bull. Math. Biophysics, 17:257--278
*FitzHugh R. (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophysical J. 1:445-466
*FitzHugh R. (1969) Mathematical models of excitation and propagation in nerve. Chapter 1 (pp. 1-85 in H.P. Schwan, ed. Biological Engineering, McGraw-Hill Book Co., N.Y.)
*Nagumo J., Arimoto S., and Yoshizawa S. (1962) An active pulse transmission line simulating nerve axon. Proc IRE. 50:2061–2070.

External links

* [http://scholarpedia.org/article/FitzHugh-Nagumo_Model FitzHugh-Nagumo model on Scholarpedia]
* [http://thevirtualheart.org/FHNindex.html Interactive FitzHugh-Nagumo.] Java applet, includes phase space and parameters can be changed at any time.
* [http://thevirtualheart.org/FHN1dindex.html Interactive FitzHugh-Nagumo in 1D. ] Java applet to simulate 1D waves propagating in a ring. Parameters can also be changed at any time.
* [http://thevirtualheart.org/FHN2dindex.html Interactive FitzHugh-Nagumo in 2D.] Java applet to simulate 2D waves including spiral waves. Parameters can also be changed at any time.