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.

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

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