Nonlinear Dynamics

, Volume 95, Issue 2, pp 1067–1078 | Cite as

Effect of electromagnetic radiation on the dynamics of spatiotemporal patterns in memristor-based neuronal network

  • Clovis Ntahkie TakemboEmail author
  • Alain Mvogo
  • Henri Paul Ekobena Fouda
  • Timoléon Crépin Kofané
Original Paper


Modulational instability, as a mechanism of wave trains and soliton formation in biological system, is explored in the frame work of the new FitzHugh–Nagumo model. This model considered chain networks with memristive synaptic connection between adjacent neurons. This connection replaces the synaptic coupling and neurons bridged for signal exchange. From the physical law of electromagnetic induction, we interpret the traditional current term as magnetic flux variable. Magnetic flux is used to describe time-varying electromagnetic field setup in cells as a result of internal bioelectricity of the nervous system as well as when cells are exposed to external electromagnetic field. We reduced the whole network dynamical equations through multi-scale expansion to obtain a single differential–difference nonlinear equation of Schrödinger type. Linear stability is then performed with emphasis on memristive synaptic coupling. The conditions under which uniform plane waves propagating in the network become stable or unstable under small perturbation are calculated and plotted. Numerical experiments confirm our analytical predictions as the network supports localized mode excitations, spike-like, identified as quasi-periodic patterns, with some features of synchronization. It is confirmed that under strong electromagnetic radiation, the propagating waves encountered turbulent electrical activities, with patterns breakdown into a homogeneous state. This disordered state, collapse and instability of traveling pulse are monitored and analyzed using the sampled time series for membrane potential. It decreases to quiescent state under strong electromagnetic field. This could provide some guidance to understanding some neurodegenerative manifestations linked with high radiation exposure.


Neural networks Memristive synapse Electromagnetic radiation Wave patterns Brain seizures 


Compliance with ethical standards

Conflict of interest

The authors of this paper declare that they have no conflict of interest concerning the publication of this manuscript.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Clovis Ntahkie Takembo
    • 1
    • 2
    Email author
  • Alain Mvogo
    • 1
    • 2
  • Henri Paul Ekobena Fouda
    • 1
    • 2
  • Timoléon Crépin Kofané
    • 2
    • 3
  1. 1.Laboratory of Biophysics, Department of Physics, Faculty of ScienceUniversity of Yaounde IYaoundéCameroon
  2. 2.Laboratory of Mecanics, Department of Physics, Faculty of ScienceUniversity of Yaounde IYaoundéCameroon
  3. 3.The Abdus Salam International Centre for Theoretical PhysicsTriesteItaly

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