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Chaos / Volume 21 / Issue 4 / FOCUS ISSUE: NONLINEAR AND STOCHASTIC PHYSICS IN BIOLOGY

Chaos 21, 047511 (2011); http://dx.doi.org/10.1063/1.3665200 (11 pages)

Variability of spatio-temporal patterns in non-homogeneous rings of spiking neurons

Serhiy Yanchuk1, Przemyslaw Perlikowski2, Oleksandr V. Popovych3, and Peter A. Tass3,4

1Institute of Mathematics, Humboldt University of Berlin, 10099 Berlin, Germany
2Division of Dynamics, Technical University of Lodz, 90-924 Lodz, Poland
3Institute of Neurosciences and Medicine - Neuromodulation (INM-7), Research Center Jülich, 52425 Jülich, Germany
4Department of Stereotaxic and Functional Neurosurgery, University Hospital, 50924 Cologne, Germany

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(Received 30 August 2011; accepted 11 November 2011; published online 29 December 2011)

We show that a ring of unidirectionally delay-coupled spiking neurons may possess a multitude of stable spiking patterns and provide a constructive algorithm for generating a desired spiking pattern. More specifically, for a given time-periodic pattern, in which each neuron fires once within the pattern period at a predefined time moment, we provide the coupling delays and/or coupling strengths leading to this particular pattern. The considered homogeneous networks demonstrate a great multistability of various travelling time- and space-periodic waves which can propagate either along the direction of coupling or in opposite direction. Such a multistability significantly enhances the variability of possible spatio-temporal patterns and potentially increases the coding capability of oscillatory neuronal loops. We illustrate our results using FitzHugh-Nagumo neurons interacting via excitatory chemical synapses as well as limit-cycle oscillators.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE MODELS
  3. TRAVELLING FRONTS IN HOMOGENEOUSLY COUPLED SYSTEMS
    1. Properties of travelling waves in LC coupled systems
    2. Perturbations of backward propagating fronts
    3. Travelling waves in coupled FitzHugh-Nagumo neurons
  4. VARIABILITY OF SPIKE PATTERNS IN NON-HOMOGENEOUS RINGS
    1. Firing patterns induced by inhomogeneous coupling delays
    2. Firing patterns induced by inhomogeneous synaptic weights
    3. Cooperative effect of inhomogeneous delays and synaptic weights
    4. Basins of attraction
    5. Firing patterns induced by inhomogeneous internal parameters of oscillators
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

neurophysiology, spatiotemporal phenomena

PACS

  • 87.19.lg

    Synapses: chemical and electrical (gap junctions)

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3665200

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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