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Dynamics of map-based neuronal network with modified spike-timing-dependent plasticity

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Abstract

The effect of adaptive coupling is studied in a neural network of randomly-coupled Rulkov maps. As an adaptive mechanism, we propose a modified spike-timing-dependent plasticity (STDP) rule with implemented homeostatic property. The comparison of the results of classical and modified STDP shows that the implication of homeostatic property results in significant changes in the network dynamics. Moreover, the neural network with modified STPD demonstrates much more pronounced dynamical changes when internal noise and stimulus amplitudes are varied. The use of the modified rule also leads to decreasing coherence and characteristic correlation time in the system.

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References

  1. O.V. Maslennikov, V.I. Nekorkin, Phys. Usp. 60, 694 (2017)

    Article  ADS  Google Scholar 

  2. B. Draganski, C. Gaser, V. Busch, G. Schuierer, U. Bogdahn, A. May, Nature 427, 311 (2004)

    Article  ADS  Google Scholar 

  3. H.J. Hwang, K. Kwon, C.H. Im, J. Neurosci. Methods 179, 150 (2009)

    Article  Google Scholar 

  4. V.A. Maksimenko, S. Heukelum, V.V. Makarov, J. Kelderhuis, A. Luttjohann, A.A. Koronovskii, A.E. Hramov, G. van Luijtelaar, Sci. Rep. 7, 2487 (2017)

    Article  ADS  Google Scholar 

  5. A.M. Dollar, H. Herr, IEEE Trans. Robot. 24, 144 (2008)

    Article  Google Scholar 

  6. M. Haugland, T. Sinkjær, Technol. Health. Care 7, 393 (1999)

    Google Scholar 

  7. N.M. Nasrabadi, J. Electron. Imaging 16, 049901 (2007)

    Article  ADS  Google Scholar 

  8. D. Hu, H. Cao, Commun. Nonlinear Sci. Numer. Simul. 35, 105 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  9. H. Sun, H. Cao, Commun. Nonlinear Sci. Numer. Simul. 40, 15 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  10. S. Boccaletti, A.N. Pisarchik, C.I. del Genio, A. Amann, Synchronization: from coupled systems to complex networks (Cambridge University Press, 2018)

  11. A.V. Andreev, V.V. Makarov, A.E. Runnova, A.N. Pisarchik, A.E. Hramov, Chaos Solitons Fractals 106, 80 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  12. A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 775 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  13. S. Song, K.D. Miller, L.F. Abbott, Nat. Neurosci. 3, 919 (2000)

    Article  Google Scholar 

  14. C. Clopath, L. Busing, E. Vasilaki, W. Gerstner, Nat. Neurosci. 13, 344 (2010)

    Article  Google Scholar 

  15. D.E. Shulz, D.E. Feldman, in Neural circuit development and function in the brain (Academic Press, 2013), p. 155

  16. E.M. Izhikevich, G.M. Edelman, Proc. Natl. Acad. Sci. U.S.A. 105, 3593 (2008)

    Article  ADS  Google Scholar 

  17. P. Arena, S. De Fiore, L. Patanè, M. Pollino, C. Ventura, in Proceedings of the 2010 International Joint Conference on Neural Networks (2010) pp. 1–8

  18. N. Shibuya, C. Unsworth, Y. Uwate, Y. Nishio, in IEEE Workshop on Nonlinear Circuit Networks (2013), pp. 61–64

  19. R.R. Borges, F.S. Borges, E.L. Lameua, A.M. Batistaa, K.C. Iarosz, I.L. Caldas, R.L. Viana, M.A.F. Sanjuán, Commun. Nonlinear Sci. Numer. Simul. 34, 12 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  20. N.F. Rulkov, I. Timofeev, M. Bazhenov, J. Comput. Neurosci. 17, 203 (2004)

    Article  Google Scholar 

  21. D. Hu, H. Cao, Commun. Nonlinear Sci. Numer. Simulat. 35, 105 (2016)

    Article  Google Scholar 

  22. Q. Wang, M. Perc, Z. Duan, G. Chen, Phys. Rev. E 80, 026206 (2009)

    Article  ADS  Google Scholar 

  23. J.M. Sausedo-Solorio, A.N. Pisarchik, Eur. Phys. J. Special Topics 226, 1911 (2017)

    Article  ADS  Google Scholar 

  24. J.S. Bendat, A.G. Piersol, Random data: analysis and measurement procedures (John Wiley and Sons, New York, Sydney, London, 2011)

  25. A.L. Shilnikov, N.F. Rulkov, Int. J. Bifurc. Chaos 13, 3325 (2003)

    Article  Google Scholar 

  26. W. Wallace, M.F. Bear, J. Neurosci. 24, 6928 (2004)

    Article  Google Scholar 

  27. V.V. Makarov, A.A. Koronovskii, V.A. Maksimenko, A.E. Hramov, O.I. Moskalenko, J.M. Buldú, S. Boccaletti, Chaos Solitons Fractals 84, 23 (2016)

    Article  ADS  Google Scholar 

  28. R. Gutierrez, A. Amann, S. Assenza, J. Gomez-Gardenes, V. Latora, S. Boccaletti, Phys. Rev. Lett. 107, 234103 (2011)

    Article  ADS  Google Scholar 

  29. A.J. Watt, N.S. Desai, Front. Synaptic Neurosci. 2, 5 (2010)

    Article  Google Scholar 

  30. E. Marder, J.M. Goaillard, Nature Rev. Neurosci. 7, 563 (2006)

    Article  Google Scholar 

  31. S. Skorheim, P. Lonjers, M. Bazhenov, PLoS One 9, e90821 (2014)

    Article  ADS  Google Scholar 

  32. N. Kasabov, K. Dhoble, N. Nuntalid, G. Indiveri, Neural Netw. 41, 188 (2013)

    Article  Google Scholar 

  33. G. Indiveri, E. Chicca, R. Douglas, IEEE Trans. Neural Netw. 17, 211 (2006)

    Article  Google Scholar 

Download references

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Correspondence to A. E. Hramov.

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Andreev, A.V., Pitsik, E.N., Makarov, V.V. et al. Dynamics of map-based neuronal network with modified spike-timing-dependent plasticity. Eur. Phys. J. Spec. Top. 227, 1029–1038 (2018). https://doi.org/10.1140/epjst/e2018-800036-5

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  • DOI: https://doi.org/10.1140/epjst/e2018-800036-5

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