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Edited by: Stephen Coombes, Yulia Timofeeva

Although mathematical work on Neurodynamics has increased in recent years, the study of heterogeneity, noise, delays, and plasticity needs much further attention.  A firmer mathematical framework for treating dynamical systems with these attributes will pave the way for a more comprehensive understanding of the dynamic states of biological neural networks, and their role in facilitating natural computation.  This special issue reports activity in this area as presented at a three day meeting at Edinburgh in March 2012.

  1. In this paper, we study the dynamics of a quadratic integrate-and-fire neuron, spiking in the gamma (30–100 Hz) range, coupled to a delta/theta frequency (1–8 Hz) neural oscillator. Using analytical and semian...

    Authors: Lorenzo Fontolan, Maciej Krupa, Alexandre Hyafil and Boris Gutkin
    Citation: The Journal of Mathematical Neuroscience 2013 3:16
  2. Oscillations in the basal ganglia are an active area of research and have been shown to relate to the hypokinetic motor symptoms of Parkinson’s disease. We study oscillations in a multi-channel mean field mode...

    Authors: Robert Merrison-Hort, Nada Yousif, Felix Njap, Ulrich G Hofmann, Oleksandr Burylko and Roman Borisyuk
    Citation: The Journal of Mathematical Neuroscience 2013 3:14
  3. The phase response curve (PRC) is a powerful tool to study the effect of a perturbation on the phase of an oscillator, assuming that all the dynamics can be explained by the phase variable. However, factors li...

    Authors: Oriol Castejón, Antoni Guillamon and Gemma Huguet
    Citation: The Journal of Mathematical Neuroscience 2013 3:13
  4. We investigate firing threshold manifolds in a mathematical model of an excitable neuron. The model analyzed investigates the phenomenon of post-inhibitory rebound spiking due to propofol anesthesia and is ada...

    Authors: John Mitry, Michelle McCarthy, Nancy Kopell and Martin Wechselberger
    Citation: The Journal of Mathematical Neuroscience 2013 3:12
  5. “Neurodynamics” is an interdisciplinary area of mathematics where dynamical systems theory (deterministic and stochastic) is the primary tool for elucidating the fundamental mechanisms responsible for the beha...

    Authors: Stephen Coombes and Yulia Timofeeva
    Citation: The Journal of Mathematical Neuroscience 2013 3:10