Mihail Popa, Adelina Georgescu, Carmen Rocşoreanu, “A Lie algebra of a differential generalized FitzHugh–Nagumo system”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, Number 1,Pages <nobr>18

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Research articles

A Lie algebra of a differential generalized FitzHugh–Nagumo system

Mihail Popa^a, Adelina Georgescu^b, Carmen Rocşoreanu^c

^a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova
^b University of Piteşti, Department of Mathematics, Piteşti, România
^c University of Craiova, Department of Mathematics, Craiova, România

Abstract: 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.

Keywords and phrases: Lie algebra, group, orbit, equilibria, phase dynamics, bifurcation.

MSC: 34C14, 34C15, 34C23, 34A47

Received: 17.10.2002

Language: English