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Slow dynamics and regularization phenomena in ensembles of chaotic neurons

Author

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  • Rabinovich, M.I.
  • Varona, P.
  • Torres, J.J.
  • Huerta, R.
  • Abarbanel, H.D.I.

Abstract

We have explored the role of calcium concentration dynamics in the generation of chaos and in the regularization of the bursting oscillations using a minimal neural circuit of two coupled model neurons. In regions of the control parameter space where the slowest component, namely the calcium concentration in the endoplasmic reticulum, weakly depends on the other variables, this model is analogous to three dimensional systems as found in [1] or [2]. These are minimal models that describe the fundamental characteristics of the chaotic spiking-bursting behavior observed in real neurons. We have investigated different regimes of cooperative behavior in large assemblies of such units using lattice of non-identical Hindmarsh-Rose neurons electrically coupled with parameters chosen randomly inside the chaotic region. We study the regularization mechanisms in large assemblies and the development of several spatio-temporal patterns as a function of the interconnectivity among nearest neighbors.

Suggested Citation

  • Rabinovich, M.I. & Varona, P. & Torres, J.J. & Huerta, R. & Abarbanel, H.D.I., 1999. "Slow dynamics and regularization phenomena in ensembles of chaotic neurons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 405-414.
    • Handle: RePEc:eee:phsmap:v:263:y:1999:i:1:p:405-414
    DOI: 10.1016/S0378-4371(98)00528-7
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    References listed on IDEAS

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    1. Alexander Rabinovich & Sebastian Monserrat, 1998. "Generation of Meteorological Tsunamis (Large Amplitude Seiches) Near the Balearic and Kuril Islands," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 18(1), pages 27-55, July.
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    Cited by:

    1. Wu, Quanjun & Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2009. "Impulsive control and synchronization of chaotic Hindmarsh–Rose models for neuronal activity," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2706-2715.
    2. Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2007. "Physical interpretation and theory of existence of cluster structures in lattices of dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1082-1104.

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