Geodesic
A Lie algebra of a differential generalized FitzHugh–Nagumo system
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2003), pp. 18-30 
Mihail Popa; Adelina Georgescu; Carmen Rocşoreanu. A Lie algebra of a differential generalized FitzHugh–Nagumo system. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2003), pp. 18-30. http://geodesic.mathdoc.fr/item/BASM_2003_1_a2/
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     title = {A~Lie algebra of a~differential generalized {FitzHugh{\textendash}Nagumo} system},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Some Lie algebra admissible for a generalized FitzHugh-Nagumo (F-N) system is constructed. Then this algebra is used to classify the dimension of the $Aff_3(2,R)$-orbits and to derive the four canonical systems corresponding to orbits of dimension equal to 1 or 2. The phase dynamics generated by these systems is studied and is found to differ qualitatively from the dynamics generated by the classical F-N system the $Aff_3(2,R)$-orbits of which are of dimension 3. A dynamic bifurcation diagram is also presented.

[1] Rocşoreanu C., Georgescu A., Giurgiţeanu N., FitzHugh-Nagumo model, Kluwer, Dordrecht, 2000

[2] Popa M. N., Applications of algebras to differential systems, Academy of Sciences of Moldova, Chişinău, 2001 (in Russian) | Zbl

[3] Academic Press, 1982 | MR | Zbl

[4] Murray J. D., Mathematical biology, Springer, Berlin, 1993 | MR

[5] Kuznetsov Yu., Elements of applied bifurcation theory, Springer, New York, 1995 | MR