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