Generalized Fitzhugh– Nagumo equation; Polynomial differential quadrature method; Numerical solutions; Runge–Kutta method Abstract In this paper, polynomial differential quadrature method (PDQM) is applied to find the numerical solution of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients in one dimensional space. The PDQM reduces the problem into a system of first order...

We investigate the organization of mixed-mode oscillations in the self-coupled FitzHugh-Nagumo system. These types of oscillations can be explained as a combination of relaxation oscillations and small-amplitude oscillations controlled by canard solutions that are associated with a folded singularity on a critical manifold. The self-coupled FitzHugh-Nagumo system has a cubic critical manifold f...

The effective noise intensity D that is used to evaluate theoretical value of 〈C1〉 throughout the original paper is inaccurate. In Sec. III A, we derived the piecewise-linear FitzHugh-Nagumo (plFHN) neuron model, and we introduced the noise scaling ξ (t) → 7τξ (t̃) in correspondence with the time scaling t → 7τ t̃ . However, the noise should be scaled as ξ (t) → √7τξ (t̃). Therefore, the plFHN neu...

Figure 1: Scroll wave turbulence developed from a scroll with a curved filament. Simulation of FitzHugh-Nagumo model in 3D, parameters as in (Biktashev 1998). Red surfaces are fronts (u=0,v<0) blue surfaces are backs (u=0,v>0) of excitation waves, and yellow lines are singularities (u=0,v=0)rotating around slowly moving scroll filaments, where u,v are respectively the activator and inhibitor fi...

We show that firing activity (spiking) can be regularized by noise in a FitzHugh-Nagumo (FHN) neuron model when operating slightly beyond the supercritical Hopf bifurcation (in the "canard" region). We also provide the conditions for imperfect phase locking between interspike intervals and low amplitude quasiharmonic oscillations. For the imperfect phase locking no need exists of an external si...