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Initial boundary value problems for coupled nerve fibres

Published online by Cambridge University Press:  20 January 2009

P. Grindrod
P. Grindrod
Affiliation:
Department of Mathematical Sciences, The UniversityDundee
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In this paper we analyse the electrical behaviour within systems of long and short coupled nerve axons by using a geometric approach to obtain a priori bounds on solutions. In [4[ we developed a general model for a bundle of n-uniform unmylinated nerve fibres. If FitzHugh-Nagumo dynamics, [3[ are used to describe the ionic membrane currents, then the model takes the form

Here W=(w1,…wn)T denotes the membrane action potentials for each fibre in the bundle and Z=(Z1,…Zn)T represents the recovery variables for each fibre, which control the return to the resting equilibrium after any transmission of signals.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 2 , June 1985 , pp. 249 - 269
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

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