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. 2019 Dec 4;9:18335. doi: 10.1038/s41598-019-54444-z

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© The Author(s) 2019

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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Properties of analytic versus filtered LFPs. Properties of the envelope and phase of the excitatory and inhibitory LFPs in Eqs. 1 and 2 obtained via the analytic signal technique (see Methods). Shown are the distributions of (a) the ratio of the envelopes of the inhibitory and excitatory LFPs (I/E), (b) the phase difference between E and I LFPs (c), the instantaneous frequency of the excitatory LFP, (d) the instantaneous frequency of the inhibitory LFP, (e) the envelope of the excitatory LFP envelope, and (f) the envelope of the inhibitory LFP. For all panels, distributions in black come from exact numerical simulations of the full nonlinear stochastic Wilson-Cowan neural network with 2-state neurons (Fig. 1 bottom panel), while those in red come from the approximate linear stochastic model, Eqs. 1 and 2. In panels (a–d), the vertical blue lines represent analytical predictions of the means of those distributions (Methods). For panels (a–b), the means were computed using Eq. 19, while for panels (c–d) we use the expression of ω₀ right after Eq. 6. The instantaneous frequencies (Panels (e–f)) are obtained as in³⁸.