Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
The purpose of this study is to classify the dynamics of the FitzHugh-Nagumo system \[\dot{x}=z, \quad \dot{y}=b(x-dy), \quad \dot{z}=x(x-1)(x-a)+y+cz\] having invariant algebraic surfaces. The system has four different types of invariant algebraic surfaces. The dynamics of the FitzHugh-Nagumo system having two of these classes of invariant algebraic surfaces has been studied in [\textit{C. Valls}, J. Nonlinear Math. Phys. 26, No. 4, 569--578 (2019; Zbl 1418.34072)]. Applying the quasi-homogeneous directional blow-up and the Poincaré compactification, the authors describe the dynamics of the FitzHugh-Nagumo system having the two remaining classes of invariant algebraic surfaces. Moreover, it is proved that these FitzHugh-Nagumo systems have no limit cycles.
scientific article; zbMATH DE number 7349782
scientific article