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Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

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Abstract

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave.

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Acknowledgements

This publication was based on work supported in part by the National Science Foundation (DMS-0813677) and by Award No KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST). PCB was also partially supported by the Royal Society-Wolfson Foundation. We would like to thank Carlo Laing for helpful conversations regarding numerical simulations. We also thank Bard Ermentrout for highlighting issues regarding bump stability calculations in the high-gain limit.

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  1. Department of Mathematics, University of Utah, Salt Lake City, UT, 84112-0090, USA

    Zachary P. Kilpatrick & Paul C. Bressloff

  2. Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford, OX1 3LB, UK

    Paul C. Bressloff

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  1. Zachary P. Kilpatrick
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Correspondence to Paul C. Bressloff.

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Kilpatrick, Z.P., Bressloff, P.C. Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression. J Comput Neurosci 28, 193–209 (2010). https://doi.org/10.1007/s10827-009-0199-6

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  • DOI: https://doi.org/10.1007/s10827-009-0199-6

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