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For: Mitry J, McCarthy M, Kopell N, Wechselberger M. Excitable neurons, firing threshold manifolds and canards. J Math Neurosci 2013;3:12. [PMID: 23945278 PMCID: PMC3819701 DOI: 10.1186/2190-8567-3-12] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2012] [Accepted: 03/20/2013] [Indexed: 05/22/2023]
Number Cited by Other Article(s)
1
Panahi S, Do Y, Hastings A, Lai YC. Rate-induced tipping in complex high-dimensional ecological networks. Proc Natl Acad Sci U S A 2023;120:e2308820120. [PMID: 38091288 PMCID: PMC10743502 DOI: 10.1073/pnas.2308820120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 11/15/2023] [Indexed: 12/24/2023]  Open
2
Penalva J, Desroches M, Teruel AE, Vich C. Slow passage through a Hopf-like bifurcation in piecewise linear systems: Application to elliptic bursting. CHAOS (WOODBURY, N.Y.) 2022;32:123109. [PMID: 36587327 DOI: 10.1063/5.0101778] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Accepted: 11/09/2022] [Indexed: 06/17/2023]
3
Cross-scale excitability in networks of quadratic integrate-and-fire neurons. PLoS Comput Biol 2022;18:e1010569. [PMID: 36191049 PMCID: PMC9560555 DOI: 10.1371/journal.pcbi.1010569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Revised: 10/13/2022] [Accepted: 09/13/2022] [Indexed: 11/05/2022]  Open
4
Köksal Ersöz E, Wendling F. Canard solutions in neural mass models: consequences on critical regimes. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2021;11:11. [PMID: 34529192 PMCID: PMC8446153 DOI: 10.1186/s13408-021-00109-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 08/17/2021] [Indexed: 05/06/2023]
5
Köksal Ersöz E, Modolo J, Bartolomei F, Wendling F. Neural mass modeling of slow-fast dynamics of seizure initiation and abortion. PLoS Comput Biol 2020;16:e1008430. [PMID: 33166277 PMCID: PMC7676664 DOI: 10.1371/journal.pcbi.1008430] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Revised: 11/19/2020] [Accepted: 10/08/2020] [Indexed: 12/31/2022]  Open
6
Köksal Ersöz E, Desroches M, Guillamon A, Rinzel J, Tabak J. Canard-induced complex oscillations in an excitatory network. J Math Biol 2020;80:2075-2107. [PMID: 32266428 DOI: 10.1007/s00285-020-01490-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2019] [Revised: 03/25/2020] [Indexed: 10/24/2022]
7
Velarde OM, Urdapilleta E, Mato G, Dellavale D. Bifurcation structure determines different phase-amplitude coupling patterns in the activity of biologically plausible neural networks. Neuroimage 2019;202:116031. [PMID: 31330244 DOI: 10.1016/j.neuroimage.2019.116031] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2019] [Revised: 07/10/2019] [Accepted: 07/16/2019] [Indexed: 12/15/2022]  Open
8
Köksal Ersöz E, Desroches M, Mirasso CR, Rodrigues S. Anticipation via canards in excitable systems. CHAOS (WOODBURY, N.Y.) 2019;29:013111. [PMID: 30709107 DOI: 10.1063/1.5050018] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2018] [Accepted: 12/19/2018] [Indexed: 06/09/2023]
9
Zhou Y, Vo T, Rotstein HG, McCarthy MM, Kopell N. M-Current Expands the Range of Gamma Frequency Inputs to Which a Neuronal Target Entrains. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2018;8:13. [PMID: 30519798 PMCID: PMC6281550 DOI: 10.1186/s13408-018-0068-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2018] [Accepted: 11/18/2018] [Indexed: 05/25/2023]
10
Shoffner S, Schnell S. Approaches for the estimation of timescales in nonlinear dynamical systems: Timescale separation in enzyme kinetics as a case study. Math Biosci 2017;287:122-129. [DOI: 10.1016/j.mbs.2016.09.001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2016] [Revised: 08/30/2016] [Accepted: 09/01/2016] [Indexed: 10/21/2022]
11
Avitabile D, Desroches M, Knobloch E. Spatiotemporal canards in neural field equations. Phys Rev E 2017;95:042205. [PMID: 28505875 DOI: 10.1103/physreve.95.042205] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2016] [Indexed: 06/07/2023]
12
Wang L, Wang H, Yu L, Chen Y. Spike-Threshold Variability Originated from Separatrix-Crossing in Neuronal Dynamics. Sci Rep 2016;6:31719. [PMID: 27546614 PMCID: PMC4992847 DOI: 10.1038/srep31719] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2016] [Accepted: 07/26/2016] [Indexed: 11/09/2022]  Open
13
Perryman C, Wieczorek S. Adapting to a changing environment: non-obvious thresholds in multi-scale systems. Proc Math Phys Eng Sci 2014;470:20140226. [PMID: 25294963 DOI: 10.1098/rspa.2014.0226] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2014] [Accepted: 07/15/2014] [Indexed: 11/12/2022]  Open
14
Tonnelier A. Threshold curve for the excitability of bidimensional spiking neurons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014;90:022701. [PMID: 25215752 DOI: 10.1103/physreve.90.022701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2014] [Indexed: 06/03/2023]
15
Dahlem MA, Schumacher J, Hübel N. Linking a genetic defect in migraine to spreading depression in a computational model. PeerJ 2014;2:e379. [PMID: 24860703 PMCID: PMC4017887 DOI: 10.7717/peerj.379] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2014] [Accepted: 04/23/2014] [Indexed: 11/20/2022]  Open
16
Cannon J, McCarthy MM, Lee S, Lee J, Börgers C, Whittington MA, Kopell N. Neurosystems: brain rhythms and cognitive processing. Eur J Neurosci 2014;39:705-19. [PMID: 24329933 PMCID: PMC4916881 DOI: 10.1111/ejn.12453] [Citation(s) in RCA: 130] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2013] [Revised: 10/29/2013] [Accepted: 11/11/2013] [Indexed: 11/30/2022]
17
Weinberg SH. High-frequency stimulation of excitable cells and networks. PLoS One 2013;8:e81402. [PMID: 24278435 PMCID: PMC3835437 DOI: 10.1371/journal.pone.0081402] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2013] [Accepted: 10/22/2013] [Indexed: 11/27/2022]  Open
18
Yu N, Li YX, Kuske R. A computational study of spike time reliability in two types of threshold dynamics. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2013;3:11. [PMID: 23945258 PMCID: PMC3849148 DOI: 10.1186/2190-8567-3-11] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/20/2012] [Accepted: 04/23/2013] [Indexed: 06/02/2023]
19
Coombes S, Timofeeva Y. Editorial for special issue on neurodynamics. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2013;3:10. [PMID: 23945204 PMCID: PMC3849104 DOI: 10.1186/2190-8567-3-10] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2013] [Accepted: 06/18/2013] [Indexed: 06/02/2023]
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