Advertisement

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

Abstract

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.

Keywords

Neural networks Memristive synapse Electromagnetic radiation Wave patterns Brain seizures 

Notes

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.

References

  1. 1.
    Sobel, E., Davanipour, Z.: Electromagnetic field exposure may cause increased production of amyloid silly and eventually lead to Alzheimer’s disease. Neurology 47, 1594 (1996)CrossRefGoogle Scholar
  2. 2.
    Clarke, D., Sokoloff, L.: Basic neurochemistry: molecular, cellular and medical aspects. In: Siegel, G.J. (ed.) Lippincott-Raven, Philadelphia (1999)Google Scholar
  3. 3.
    Johansen, C.: Exposure to electromagnetic field fields and risk of central nervous system disease in ultility workers. Epidemiology 11, 539 (2000)CrossRefGoogle Scholar
  4. 4.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond.) 117, 500–544 (1952)CrossRefGoogle Scholar
  5. 5.
    Fan, L., Quirui, L., Guo, H.: Simulating the electric activity of FitzHugh–Nagumo neuron by using Josephson junction model. Nonlinear Dyn. 69, 2169–2179 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Eteme, A.S., Tabi, C.B., Mohamadou, A.: Long-range patterns in Hindmarsh–Rose Networks. Commun. Nonlinear Sci. Numer. Simul. 43, 211 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gu, H.G., Pan, B.B.: A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model. Nonlinear Dyn. 81, 2107–2126 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hilgetag, C.C., Kaiser, M.: Clustered organization of cortical connectivity. Neuroinformatics 2, 353 (2004)CrossRefGoogle Scholar
  9. 9.
    Stankovski, T., Pereira, T.: Coupling functions: universal insights into dynamical interaction mechanisms. Rev. Mod. Phys. 89, 045001 (2017)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Song, X.L., Wang, C.N., Ma, J., et al.: Transition of electric activity of neurons induced by chemical and electric autapses. Sci. China Tech. Sci. 58, 1007–14 (2015)CrossRefGoogle Scholar
  11. 11.
    Gosak, M., Marhl, M., Perc, M.: Pacemaker-guided noise-induced spatial periodicity in excitable media. Physica D 238, 506–15 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Yilmaz, E., Ozer, M., Baysal, V., et al.: Autapse-induced multiple coherence resonance in single neurons and neuronal networks. Sci. Rep. 6, 30914 (2016)CrossRefGoogle Scholar
  13. 13.
    Wang, C.N., Guo, S.L., Xu, Y., et al.: Formation of autapse connected to neuron and its biological function. Complexity 2017, 5436737 (2017)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Lisi, A., Ciotti, M.T., Ledda, M., et al.: Exposure to 50 Hz electromagnetic radiation promote early maturation and differentiation in newborn rat cerebellar granule neurons. J. Cell. Phys. 204(2), 532–538 (2005)CrossRefGoogle Scholar
  15. 15.
    Xu, S.C., Zhou, Z., Zhang, L., et al.: Exposure to 1800 MHz radiofrequency radiation induces oxidative damage to mitochondrial DNA in primary cultured neurons. Brain Res. 1311, 189–196 (2010)CrossRefGoogle Scholar
  16. 16.
    Takembo, C.N., Mvogo, A., Ekobena, H.P., et al.: Modulated wave formation in myocardial cells under electromagnetic radiation. Int. J. Mod. Phys. B 32, 1850165 (2018)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhao, R., Zhang, S.Z., Xu, Z.P., et al.: Studying gene expression profile of rat neuron exposed to 1800 MHz radiofrequency electromagnetic fields with cDNA microassay. Toxicology 235(3), 167–175 (2007)CrossRefGoogle Scholar
  18. 18.
    Masuda, H., Ushiyama, A., Takahashi, M., et al.: Effects of 915 MHz electromagnetic-field radiation in TEM cell on the blood-brain barrier and neurons in the rat brain. Radiat. Res. 172(1), 66–73 (2009)CrossRefGoogle Scholar
  19. 19.
    Wu, F.Q., Wang, C.N., Xu, Y., et al.: Model of electrical activity in cardiac tissue under electromagnetic induction. Sci. Rep. 6, 28 (2016)CrossRefGoogle Scholar
  20. 20.
    Ge, M., Jia, Y., Xu, Y., et al.: Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation. Nonlinear Dyn. 91, 515–23 (2018)CrossRefGoogle Scholar
  21. 21.
    Xu, Y., Ying, H., et al.: Autaptic regulation of electrical activities in neuron under electromagnetic induction. Sci. Rep. 7, 43452 (2016)CrossRefGoogle Scholar
  22. 22.
    Zhang, G., Wang, C.: Investigation of dynamical behaviors of neurons driven by memristive synapse. Chaos Solitons Fractals 108, 15–24 (2018)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Benjamin, T.B., Feir, J.E.: The disintegration of wave trains on deep water Part 1. Theory J. Fluid Mech. 27, 417 (1967)CrossRefzbMATHGoogle Scholar
  24. 24.
    Moukam, F.M., Inack, E.M., Yamakou, E.M.: Localized nonlinear excitations in diffusive Hindmarsh–Rose neural networks. Phys. Rev. E 89, 052919 (2014)CrossRefGoogle Scholar
  25. 25.
    Eteme, A.S., Tabi, C.B., Mohamadou, A.: Synchronized nonlinear patterns in electrically coupled Hindmarsh-Rose neural networks with long-range diffusive interactions. Chaos Solitons Fractals 104, 813–826 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    FitzHugh, R.: The biophysical society all rights reserved. Biophys. J. 1, 445–466 (1961)CrossRefGoogle Scholar
  27. 27.
    Nagumo, J., Arimoto, S., Yoshizawa, S., et al.: An active pulse transmission line simulating nerve axon. Proc. IRE 50, 2061–2070 (1962)CrossRefGoogle Scholar
  28. 28.
    Kanamaru, T., Okabe, Y.: Associative memory retrival induced by influctuations in a pulsed neural network. Phys. Rev. E 62, 2629 (2000)CrossRefGoogle Scholar
  29. 29.
    Lv, M., Wang, C.N., Ren, G.D., et al.: Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85, 1479–1490 (2016)CrossRefGoogle Scholar
  30. 30.
    Mvogo, A., Takembo, C.N., Ekobena, H.P., et al.: Pattern formation in diffusive excitable systems under magnetic flow effects. Phys. Lett. A 381, 2264–2271 (2017)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Xu, Y., Jia, Y.: Synchronization between neurons coupled by memristor. Chaos Soliton Fractals 104, 435–442 (2017)CrossRefGoogle Scholar
  32. 32.
    Xu, F., Zhang, J., Fang, T., et al.: Synchronous dynamics in neural system coupled with memristive synapse. Nonlinear Dyn. 92, 1395–1402 (2018)CrossRefGoogle Scholar
  33. 33.
    Leon, J., Manna, M.: Multiscale analysis of discrete nonlinear evolution equations. J. Phys. A Math. Gen. 32, 2845 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Leon, J., Manna, M.: Discrete instability in nonlinear lattices. Phys. Rev. Lett. 83, 2324 (1999)CrossRefGoogle Scholar
  35. 35.
    Tabi, C.B., Maïna, I., Mohamadou, A., et al.: Long-range intercellular \(Ca^{2+}\) wave patterns. Phys. A 435, 1–14 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Terman, D., Bose, A., Kopell, N.: Functinal reorganization in thalamocortical networks: Transition spindling and delta sleep rhythms. Proc. Natl. Acad. Sci. USA 93, 15417–15422 (1996)CrossRefGoogle Scholar
  37. 37.
    Battaglia, D., Brunel, N., Hansel, D.: Temporal decorrelation of collective oscillations in neural networks with local inhibition and long-range excitation. Phys. Rev. Lett. 99, 238106 (2007)CrossRefGoogle Scholar
  38. 38.
    Ribeiro, T.L., Copelli, : Deterministic excitable media under Poisson drive: power law responses, spiral waves, and dynamic range. Phys. Rev. E 77, 051911 (2008)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Lewis, T.: NIMBIOS Workshop on Synchrony, April 11 (2011)Google Scholar
  40. 40.
    Morell, M.J.: Responsive cortical stimulation for the treatment of medically intractable partial epilepsy. Neurology 77, 1295 (2011)CrossRefGoogle Scholar
  41. 41.
    Rubin, J.E., Terman, D.: High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. J. Comput. Neurosci. 16, 211 (2004)CrossRefGoogle Scholar
  42. 42.
    Robinson, P.A., Rennie, C.J., Rowe, D.L.: Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys. Rev. E 65, 041924 (2002)CrossRefGoogle Scholar
  43. 43.
    Ma, J., Wu, F., Hayat, T., et al.: Electromagnetic induction and radition-induced abnormality of wave propagation in excitable media. Physica A 486, 508–516 (2017)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Lv, M., Ma, J.: Multiple modes of electrical activities of neurons under electromagnetic radiation. Neurocomputing 205, 375–81 (2016)CrossRefGoogle Scholar
  45. 45.
    Swadlow, H.A., Gusev, A.G.: The impact of ’bursting’ thalamic impulses at a neocortical synapse. Nat. Neurosci. 4, 402 (2001)CrossRefGoogle Scholar

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

Personalised recommendations