Engineering dissipative chirped solitons in the cardiac tissue under electromagnetic induction

Abstract

This work deals with the engineering dissipative chirped solitary waves in the cardiac tissue under electromagnetic induction. Employing the a two-dimensional Ginzburg-Landau (GL) equation describing the spatiotemporal evolution of transmembrane potential in cardiac cells under magnetic flow effect, we use the phase imprint technique to reduce the model equation into a derivative GL equation (alias chirping model equation) that allow us to investigate the dynamics of dissipative chirp solitary wave propagating through a cardiac tissue. The baseband modulational instability (MI) of the chirping model is investigated and the analytical expression of the MI growth rate is derived. In the baseband MI regime, we use the approximative solitonlike solution of the chirping model to investigate the dynamics of transmembrane potential in cardiac cells. We show that the frequency chirp associated to the solitary wave is directly proportional to the wave amplitude and the nonlinear chirping parameter can be used to modulate the chirping amplitude. Also, our results show that the approximate solution of the chirping model can be used to generate bright (dissipative) solitons, dark solitons, breather solitons and first-order rogue wave in the cardiac cell under electromagnetic induction. Our theoretical results are confirmed by numerical simulations. The results of this work can motivate the investigations of qualitative new phenomena in the presence of large dissipation.