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Suppression of anomalous synchronization and nonstationary behavior of neural network under small-world topology

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  • Boaretto, B.R.R.
  • Budzinski, R.C.
  • Prado, T.L.
  • Kurths, J.
  • Lopes, S.R.

Abstract

It is known that neural networks under small-world topology can present anomalous synchronization and nonstationary behavior for weak coupling regimes. Here, we propose methods to suppress the anomalous synchronization and also to diminish the nonstationary behavior occurring in weakly coupled neural network under small-world topology. We consider a network of 2000 thermally sensitive identical neurons, based on the model of Hodgkin–Huxley in a small-world topology, with the probability of adding non local connection equal to p=0.001. Based on experimental protocols to suppress anomalous synchronization, as well as nonstationary behavior of the neural network dynamics, we make use of (i) external stimulus (pulsed current); (ii) biologic parameters changing (neuron membrane conductance changes); and (iii) body temperature changes. Quantification analysis to evaluate phase synchronization makes use of the Kuramoto’s order parameter, while recurrence quantification analysis, particularly the determinism, computed over the easily accessible mean field of network, the local field potential (LFP), is used to evaluate nonstationary states. We show that the methods proposed can control the anomalous synchronization and nonstationarity occurring for weak coupling parameter without any effect on the individual neuron dynamics, neither in the expected asymptotic synchronized states occurring for large values of the coupling parameter.

Suggested Citation

  • Boaretto, B.R.R. & Budzinski, R.C. & Prado, T.L. & Kurths, J. & Lopes, S.R., 2018. "Suppression of anomalous synchronization and nonstationary behavior of neural network under small-world topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 126-138.
    • Handle: RePEc:eee:phsmap:v:497:y:2018:i:c:p:126-138
    DOI: 10.1016/j.physa.2017.12.053
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    2. Mingwen Zheng & Lixiang Li & Haipeng Peng & Jinghua Xiao & Yixian Yang & Hui Zhao, 2016. "Finite-time stability and synchronization for memristor-based fractional-order Cohen-Grossberg neural network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(9), pages 1-11, September.
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    1. Budzinski, R.C. & Boaretto, B.R.R. & Prado, T.L. & Lopes, S.R., 2019. "Temperature dependence of phase and spike synchronization of neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 35-42.
    2. Cambraia, E.B.S.A. & Flauzino, J.V.V. & Prado, T.L. & Lopes, S.R., 2023. "Dependence on the local dynamics of a network phase synchronization process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).

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