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. 2017 Sep 20;7:11916. doi: 10.1038/s41598-017-12033-y

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(A) Frequency of the network global oscillations at the onset of the Hopf bifurcation as a function of the inhibition strength g for a network in which excitatory and inhibitory neurons have different characteristics. Longer synaptic delays give rise to slower oscillations. In this regime, the average synaptic delays are the same for excitatory and inhibitory synapses. (B) Network simulations for two different average delays. Top panels: D = 20 ms, ν _X/ν _θ,E = 0.78, g = 4; bottom panels: D = 5 ms, ν _X/ν _θ,E = 0.825, g = 5. For both parameter sets, we show the average instantaneous firing rates of excitatory (red) and inhibitory (blue) neurons, and raster plots are plotted of 50 excitatory and 50 inhibitory neurons. Other parameters: C _E = 1000, J _EE = 0.2 mV, J _EI = 034 mV.