Dynamics of the FitzHugh–Nagumo system having invariant algebraic surfaces
نویسندگان
چکیده
In this paper, we study the dynamics of FitzHugh–Nagumo system $$\dot{x}=z,\;\dot{y}=b\left( x-dy\right) ,\;\dot{z}=x\left( x-1\right) \left( x-a\right) +y+cz$$ having invariant algebraic surfaces. This has four different types The two these classes surfaces have been characterized in Valls (J Nonlinear Math Phys 26:569–578, 2019). Using quasi-homogeneous directional blow-up and Poincaré compactification, describe remaining Moreover, for systems prove that they do not limit cycles.
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ژورنال
عنوان ژورنال: Zeitschrift für Angewandte Mathematik und Physik
سال: 2021
ISSN: ['1420-9039', '0044-2275']
DOI: https://doi.org/10.1007/s00033-020-01450-1