Soliton-like nonlinear excitation in the FitzHugh–Nagumo cardiac model through the cubic–quintic complex Ginzburg–Landau equation

The article exclusively discusses how the cubic–quintic complex Ginzburg–Landau equation governs the dynamics of dissipative soliton in the FitzHugh–Nagumo model combined with linear self- and cross-diffusion terms. Then, based on the linear stability analysis, a set of equations describing the evolution of the perturbation amplitude is derived, and a detailed analysis of the modulational instability gain spectrum is presented. Moreover, the exact dissipative soliton of the cubic–quintic complex Ginzburg–Landau equation is found using Hirota’s bilinear method. Furthermore, as an input condition to our simulations, we use the obtained dissipative soliton solution to check the stability of the moving pulse solution by solving the quintic FitzHugh–Nagumo model numerically with self- and cross-diffusion terms. As a result, numerical findings are in perfect correlation with analytical investigations, thus attesting that cardiac cell dynamics through the quintic FitzHugh–Nagumo model is the support of soliton-pulse-like solutions.