On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh–Nagumo (FN) mathematical model

The Fitzhugh–Nagumo (FH) mathematical model is considered a simplification of the Hodgkin–Huxley (HH) model. This paper analyzes the non-linear dynamics of the Fitzhugh–Nagumo (FN) mathematical model, and still presents some modifications in the governing equations of the system in order to transform it into a non-ideal one (taking into account that an energy source has limited power supply). We also developed an optimal linear control design and used Sinhas’s theory for the membrane’s action potential in order to stabilize the variation of this potential.