Attraction basin of the equilibrium configuration in the FitzHugh-Nagumo model
Consider the FitzHugh-Nagumo model \[ \begin{aligned} \varepsilon{dv\over dt} &= v(1-v)(v-\alpha)- w,\\ {dw\over dt} &= v-\gamma w.\end{aligned}\tag{\(*\)} \] The author derives conditions on the coefficients \(\alpha\), \(\gamma\), \(\varepsilon\) such that \((*)\) has no limit cycle. The proof is based on the transformation of \((*)\) into a Liénard sytem of the type \[ \begin{aligned} {dx\over dt} &= y- F(x),\\ {dy\over dt} &= -g(x)\end{aligned}\tag{\(**\)} \] and on the application of a criterion due to \textit{J. Sugie} [Q. Appl. Math. 49, No. 3, 543--554 (1991; Zbl 0736.34043)] on the nonexistence of a limit cycle of system \((**)\).
scientific article; zbMATH DE number 6121145