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How single node dynamics enhances synchronization in neural networks with electrical coupling

Author

Listed:
  • Bonacini, E.
  • Burioni, R.
  • di Volo, M.
  • Groppi, M.
  • Soresina, C.
  • Vezzani, A.

Abstract

The stability of the completely synchronous state in neural networks with electrical coupling is analytically investigated applying both the Master Stability Function approach (MSF), developed by Pecora and Carroll (1998), and the Connection Graph Stability method (CGS) proposed by Belykh et al. (2004). The local dynamics is described by Morris–Lecar model for spiking neurons and by Hindmarsh–Rose model in spike, burst, irregular spike and irregular burst regimes. The combined application of both CGS and MSF methods provides an efficient estimate of the synchronization thresholds, namely bounds for the coupling strength ranges in which the synchronous state is stable. In all the considered cases, we observe that high values of coupling strength tend to synchronize the system. Furthermore, we observe a correlation between the single node attractor and the local stability properties given by MSF. The analytical results are compared with numerical simulations on a sample network, with excellent agreement.

Suggested Citation

  • Bonacini, E. & Burioni, R. & di Volo, M. & Groppi, M. & Soresina, C. & Vezzani, A., 2016. "How single node dynamics enhances synchronization in neural networks with electrical coupling," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 32-43.
    • Handle: RePEc:eee:chsofr:v:85:y:2016:i:c:p:32-43
    DOI: 10.1016/j.chaos.2016.01.009
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    References listed on IDEAS

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    1. Yu, Hongjie & Peng, Jianhua, 2006. "Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 342-348.
    2. Volman, Vladislav & Baruchi, Itay & Persi, Erez & Ben-Jacob, Eshel, 2004. "Generative modelling of regulated dynamical behavior in cultured neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 249-278.
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    Cited by:

    1. Upadhyay, Ranjit Kumar & Mondal, Argha, 2017. "Synchronization of bursting neurons with a slowly varying d. c. current," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 195-208.

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