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When Repulsive Inhibition Promotes Synchrony of Bursting Neurons: Help from the Enemy

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Advances in Dynamics, Patterns, Cognition

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 20))

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Abstract

In this chapter, we study the onset of synchronization in networks of bursting neurons coupled via both excitatory and inhibitory connections. We review our recent results and show that the addition of pairwise repulsive inhibition to excitatory networks of bursting neurons induces synchrony, in contrast to one’s expectations. Through stability analysis, we reveal the mechanism underlying this purely synergistic phenomenon and demonstrate that it originates from the transition between different types of bursting, caused by excitatory–inhibitory synaptic coupling. This effect is generic and observed in different models of bursting neurons and fast synaptic interactions. We also report a universal scaling law for the synchronization stability condition for large networks in terms of the number of excitatory and inhibitory inputs each neuron receives, regardless of the network size and topology. Our study has potential implications for understanding the emergence of abnormal synchrony in epileptic brain networks. It suggests that promoting presumably desynchronizing inhibition in an attempt to prevent seizures can have a counterproductive effect and induce abnormal synchronous firing.

Dedicated to Mikhail I. Rabinovich on the occasion of his 75th birthday

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Acknowledgements

This work was supported by the National Science Foundation (USA) under Grant No. DMS1616345 (to I.B. and R.R.), the US Army Research Office Network Science Division under Grant No. W911NF-15-1-0267 (to I.B.) and GSU Brains and Behavior program. R.R. acknowledges support as a GSU Brains and Behavior Fellow.

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Authors and Affiliations

  1. Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, GA, 30303, USA

    Reimbay Reimbayev & Kun Zhao

  2. Department of Mathematics and Statistics, Georgia State University, 30 Pryor Street, Atlanta, GA, 30303, USA

    Igor Belykh

Authors
  1. Reimbay Reimbayev
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  2. Kun Zhao
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  3. Igor Belykh
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Correspondence to Igor Belykh .

Editor information

Editors and Affiliations

  1. Pennsylvania State University, University Park, Pennsylvania, USA

    Igor S. Aranson

  2. Institute for Physics and Astronomy, University of Potsdam, Potsdam, Germany

    Arkady Pikovsky

  3. BioCircuits Institute, University of California San Diego, La Jolla, California, USA

    Nikolai F. Rulkov

  4. BioCircuits Institute, University of California San Diego, La Jolla, California, USA

    Lev S. Tsimring

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Reimbayev, R., Zhao, K., Belykh, I. (2017). When Repulsive Inhibition Promotes Synchrony of Bursting Neurons: Help from the Enemy. In: Aranson, I., Pikovsky, A., Rulkov, N., Tsimring, L. (eds) Advances in Dynamics, Patterns, Cognition. Nonlinear Systems and Complexity, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-53673-6_11

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  • DOI: https://doi.org/10.1007/978-3-319-53673-6_11

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