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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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Networks of LIF neurons with firing rate adaptation. (A) Mean-field: Coexistence regions between Q and L states, with increasing values of the strength of adaptation β. The coexistence region progressively shrinks and disappears at $β \sim$ 1.5 mV.s. Diamonds indicates the location of the simulations shown in C, D, E, F and G. Parameters: C _E = 1000, J _EE = 0.2 mV, J _EI = 0.34 mV. (B) Bifurcation diagrams (firing rates of E and I populations vs external input) for increasing values of the strength of adaptation. Solid lines: average excitatory firing rate; Dashed lines, average inhibitory firing rate. Note that the coexistence region is no longer present for β = 2.5 mV.s. (C–E) Network simulations for g = 4, ν _X = 0.76ν _θ,E, β = 0.7 mV.s, τ _A = 200 ms, D _EE = 20 ms, D _II = 10 ms. (C) Average E and I firing frequency as a function of time. The population firing frequency is averaged over 10 ms time bins. Note UP and DOWN states with irregular durations of order 1 s, and instantaneous fluctuations of E and I neurons in UP states that closely track each other. (D) Raster of 50 excitatory neurons (E) Raster of 50 inhibitory neurons. (F) Network simulations for g = 3, β = 5 mV.s, τ _A = 500 ms, ν _X = 0.8ν _θ,E. (G) Network simulations for g = 4, β = 5 mV.s, τ _A = 600 ms, ν _X = 0.8ν _θ,E.