Phase resetting and coupling of noisy neural oscillators

Journal of Computational Neuroscience
Bard Ermentrout, David Saunders

Abstract

A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phase-resetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations.

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Citations

Mar 20, 2010·Biological cybernetics·William H Nesse, Gregory A Clark
Aug 30, 2008·Journal of Computational Neuroscience·Keisuke OtaToru Aonishi
Jan 6, 2011·Journal of Computational Neuroscience·G Bard ErmentroutTheoden I Netoff
Jul 24, 2012·Journal of Computational Neuroscience·Jan R EngelbrechtMotoharu Yoshida
Jul 3, 2008·Nature Reviews. Neuroscience·William W Lytton
Jun 28, 2012·PLoS Computational Biology·M T WilsonD A Steyn-Ross
Apr 22, 2014·Progress in Brain Research·Thomas E DickKendall F Morris
May 15, 2010·Neural Networks : the Official Journal of the International Neural Network Society·Ken NakaeToshio Aoyagi
Jun 8, 2007·The European Journal of Neuroscience·Yasuhiro TsuboTomoki Fukai
Nov 4, 2010·The European Journal of Neuroscience·Julie S HaasH D I Abarbanel
Feb 28, 2014·Network : Computation in Neural Systems·Ruben Tikidji-HamburyanCarmen C Canavier
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·William H NessePaul C Bressloff
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sashi Marella, G Bard Ermentrout
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kensuke Arai, Hiroya Nakao
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Shigefumi HataHiroya Nakao
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Fred H SielingAstrid A Prinz
May 17, 2013·Physical Review Letters·Justus T C Schwabedal, Arkady Pikovsky
Sep 23, 2014·Journal of Neural Engineering·Sofia D KaramintziouKonstantina S Nikita
Dec 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Keisuke OtaToru Aonishi
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Fred H SielingAstrid A Prinz

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