FitzHugh-Nagumo model

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

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If the external stimulus I_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

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.

See also

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

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.