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Time evolution of coherent structures in networks of Hindmarch–Rose neurons

Author

Listed:
  • Mainieri, M.S.
  • Erichsen, R.
  • Brunnet, L.G.

Abstract

In the regime of partial synchronization, networks of diffusively coupled Hindmarch–Rose neurons show coherent structures developing in a region of the phase space which is wider than in the correspondent single neuron. Such structures are kept, without important changes, during several bursting periods. In this work, we study the time evolution of these structures and their dynamical stability under damage. This system may model the behavior of ensembles of neurons coupled through a bidirectional gap junction or, in a broader sense, it could also account for the molecular cascades present in the formation of flash and short time memory.

Suggested Citation

  • Mainieri, M.S. & Erichsen, R. & Brunnet, L.G., 2005. "Time evolution of coherent structures in networks of Hindmarch–Rose neurons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 663-671.
    • Handle: RePEc:eee:phsmap:v:354:y:2005:i:c:p:663-671
    DOI: 10.1016/j.physa.2005.02.014
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    References listed on IDEAS

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    1. Chaté, H. & Lemaître, A. & Marcq, Ph. & Manneville, P., 1996. "Non-trivial collective behavior in extensively-chaotic dynamical systems: an update," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 224(1), pages 447-457.
    2. Brunnet, Leonardo G. & Chaté, Hugues, 1998. "Phase coherence in chaotic oscillatory media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 257(1), pages 347-356.
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    Cited by:

    1. Agnes, E.J. & Erichsen, R. & Brunnet, L.G., 2010. "Synchronization regimes in a map-based model neural network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 651-658.
    2. Wang, Qingyun & Zheng, Yanhong & Ma, Jun, 2013. "Cooperative dynamics in neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 19-27.

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    1. Agnes, E.J. & Erichsen, R. & Brunnet, L.G., 2010. "Synchronization regimes in a map-based model neural network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 651-658.

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