Summary
Some qualitative properties of the nerve axon model due to FitzHugh are reviewed. In the case of travelling waves we study the system of ordinary differential equations cφ′=φ″+F(φ)−bψ, cψ′=φ−γψ, F (φ)=φ (φ−a) (1−φ) c>0, 0<a<1, γ≥0, b≥0 and show that the wave speed c is bounded above by (1−a). This upper bound improves a result established earlier by the author and M. W. Green. When γ≥0 we prove that there are no bounded non-constant solutions for a≥ 1/2 and b≥0. The stability of travelling waves is also considered.
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Sleeman, B.D. Fitzhugh's nerve axon equations. J. Math. Biology 2, 341–349 (1975). https://doi.org/10.1007/BF00817391
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DOI: https://doi.org/10.1007/BF00817391