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

  • Reimbay Reimbayev
  • Kun Zhao
  • Igor Belykh
Chapter
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 20)

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.

Keywords

Networks Synchronization Bursting neurons Inhibition Excitation 

Notes

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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics and Neuroscience InstituteGeorgia State UniversityAtlantaUSA
  2. 2.Department of Mathematics and StatisticsGeorgia State UniversityAtlantaUSA

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