Localized modulated wave solution of diffusive FitzHugh–Nagumo cardiac networks under magnetic flow effect

Motivated by often non-observance clinical effects attributed to some pathological heart diseases, we obtain in this paper the analytical solutions describing localized nonlinear excitations in an improved diffusive FitzHugh–Nagumo cardiac tissue model. The improved model includes the magnetic flux variable used to describe the effect of electromagnetic induction created by fluctuation in ionic concentration during the period when signals are initiated and propagated in the heart. To be consistent with physical units, memristor is used to achieve coupling between membrane potential and magnetic flux such that the induced current from electromagnetic induction is approached. Using the specific reductive perturbation approach in the semi-discrete approximation limit, we show that the whole system dynamics is governed by a modified complex Ginzburg–Landau equation, whose coefficients are dependent on memristive feedback gain. This suggests from biophysical point of view that cardiac electrical signals or waves initiated from the heart sinus node propagates in cardiac networks both in temporal and spatial dimensions in the form of a localized modulated solitonic wave thereby regulating heartbeat as powerful pacemaker. Our analytical solutions are then verified through numerical experiments.