Dynamical analysis of the FitzHugh–Nagumo oscillations through a modified Van der Pol equation with fractional-order derivative term

The nonlinear dynamics of action potentials in the FitzHugh–Nagumo model is addressed using a modified Van der Pol equation with fractional-order derivative and periodic parametric excitation. Through the averaging method, the approximately analytical and the steady-state solutions are obtained, and their existence condition and stability are investigated. Analytical calculations are confirmed numerically and one insists on the coupled effects of the parametric excitation, system parameters and fractional-order parameter to discuss the various dynamical behaviors of the studied system. Mainly, the fractional-order derivative modifies the features of the amplitude–frequency curves. This might be an efficient tool to control the dynamics of the action potentials, with important biological implications that are discussed.