Effect of electromagnetic induction on the nonlinear excitation in the FitzHugh-Nagumo cardiac model through the cubic-quintic complex Ginzburg-Landau equation

Electromagnetic induction is crucial for understanding the heart’s electrical and chemical dynamics and detecting functional abnormalities. In this study, we examine a modified FitzHugh-Nagumo (FHN) model incorporating standard diffusion and a feedback gain parameter. Through multiple-scale expansion, we derive a cubic-quintic complex Ginzburg-Landau (CQCGL) equation governing action potential dynamics, and we construct traveling wave solutions using a modified Hirota bilinear method (HBM). The feedback gain markedly affects action potentials: (i) On the left side, it reduces amplitude, period, and depolarization/repolarization duration before the transition region. (ii) On the right side, it produces a quasi-periodic structure at k0=0.64, favoring rhythm stabilization. Modulational instability (MI) analysis shows that values of k0 below or above 0.64 destabilize the system. Numerical simulations closely match the analytical results, confirming the model’s validity. Biologically, these findings highlight electromagnetic induction as a key modulator of cardiac function, influencing action potentials through ion-channel regulation and gap junction coupling, and shaping arrhythmia dynamics.