[Comp-neuro] Noise stabilization of "unstable fixed point" neuronal firing

ajmandell ajmandell at charter.net
Mon Jul 28 17:20:51 CEST 2008

  What an interesting discussion!

  Thought I'd throw in this counterintuitive analogy to the role of noise in conventional stochastic resonance in a neural membrane-like nonlinear dynamical system would be of interest. 

  (1) Real neuronal firing pattern imbedding and poincare section demonstrating stable manifold "gathering" of orbits along the unstable manifold

        So, P. Francis, J. T. Netoff, T. I.Gluckman, B. J.Schiff, S. J.

        (Unstable) Periodic orbits: a new language for neuronal dynamics; Biophys. J. 74:2776-85, 1998

        (2) Noise induced increases of orbital residence times on unstable manifold of a quasi-membrane equation and map (with neurophysiological speculations) 

        Mandell, AJ and Selz, KA . Brain stem neuronal noise and neocortical "resonance" J. Stat. Physics 70:355-373



Arnold J. Mandell, M.D.
Cielo Institute, Asheville, NC
ajmandell at charter.net
Clinical Professor of Psychiatry and Human Behavior, Emory University,
Atlanta, GA
Adjunct Professor of Mathematical Sciences, FAU, Boca Raton, FL
Founding Chairman and Professor Emeritus of Psychiatry (Neuroscience,
Pharmacology, Mathematics) UCSD, La Jolla, CA
MacArthur Prize Fellow Laureate in Theoretical Neuroscience
Humboldt Prize Fellow Laureate in Dynamical Systems

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