Nonlinear Dynamics

, Volume 95, Issue 2, pp 1079–1098 | Cite as

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

  • Clovis Ntahkie TakemboEmail author
  • Alain Mvogo
  • H. P. Ekobena Fouda
  • T. C. Kofane
Original Paper


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.


Magnetic cardiac networks Modulational instability Modified complex Ginzburg–Landau equation Soliton 


Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Clovis Ntahkie Takembo
    • 1
    Email author
  • Alain Mvogo
    • 1
  • H. P. Ekobena Fouda
    • 1
  • T. C. Kofane
    • 2
    • 3
  1. 1.Laboratory of Biophysics, Department of Physics, Faculty of ScienceUniversity of Yaounde IYaoundéCameroon
  2. 2.The Abdus Salam International Centre for Theoretical PhysicsTriesteItaly
  3. 3.Laboratory of Mechanics, Department of Physics, Faculty of ScienceUniversity of Yaounde IYaoundeCameroon

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