Stochastic dynamics of the FitzHugh-Nagumo neuron model through a modified Van der Pol equation with fractional-order term and Gaussian white noise excitation

The stochastic response of the FitzHugh-Nagumo model is addressed using a modified Van der Pol (VDP) equation with fractional-order derivative and Gaussian white noise excitation. Via generalized harmonic balance method, term related to fractional splitted into equivalent quasi-linear dissipative force restoring force, leading an VDP without derivative. The analytical solutions for are then investigated through averaging method. This thereafter compared numerical solutions, where stationary probability density function (PDF) amplitude joint PDF displacement velocity used characterized dynamical behaviors system. A satisfactory agreement found between two approaches, which confirms accuracy It also that changing parameter intensity induces P-bifurcation.