Geodesic
On Integrability of the FitzHugh – Rinzel Model
Russian journal of nonlinear dynamics, Tome 15 (2019) no. 1, pp. 13-19

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The integrability of the FitzHugh – Rinzel model is considered. This model is an example of the system of equations having the expansion of the general solution in the Puiseux series with three arbitrary constants. It is shown that the FitzHugh – Rinzel model is not integrable in the general case, but there are two formal first integrals of the system of equations for its description. Exact solutions of the FitzHugh – Rinzel system of equations are given.
Keywords: FitzHugh – Rinzel model, first integral, general solution
Mots-clés : Painlevé test, exact solution. 
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     author = {N. A. Kudryashov},
     title = {On {Integrability} of the {FitzHugh} {\textendash} {Rinzel} {Model}},
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N. A. Kudryashov. On Integrability of the FitzHugh – Rinzel Model. Russian journal of nonlinear dynamics, Tome 15 (2019) no. 1, pp. 13-19. http://geodesic.mathdoc.fr/item/ND_2019_15_1_a1/