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Neurodynamics

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. Research

    Analytical Insights on Theta-Gamma Coupled Neural Oscillators

    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...

    Lorenzo Fontolan, Maciej Krupa, Alexandre Hyafil and Boris Gutkin

    The Journal of Mathematical Neuroscience 2013 3:16

    Published on: 14 August 2013

  2. Research

    An Interactive Channel Model of the Basal Ganglia: Bifurcation Analysis Under Healthy and Parkinsonian Conditions

    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...

    Robert Merrison-Hort, Nada Yousif, Felix Njap, Ulrich G Hofmann, Oleksandr Burylko and Roman Borisyuk

    The Journal of Mathematical Neuroscience 2013 3:14

    Published on: 14 August 2013

  3. Research

    Excitable Neurons, Firing Threshold Manifolds and Canards

    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...

    John Mitry, Michelle McCarthy, Nancy Kopell and Martin Wechselberger

    The Journal of Mathematical Neuroscience 2013 3:12

    Published on: 14 August 2013

  4. Research

    Gap Junctions, Dendrites and Resonances: A Recipe for Tuning Network Dynamics

    Gap junctions, also referred to as electrical synapses, are expressed along the entire central nervous system and are important in mediating various brain rhythms in both normal and pathological states. These ...

    Yulia Timofeeva, Stephen Coombes and Davide Michieletto

    The Journal of Mathematical Neuroscience 2013 3:15

    Published on: 14 August 2013

  5. Research

    Phase-Amplitude Response Functions for Transient-State Stimuli

    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...

    Oriol Castejón, Antoni Guillamon and Gemma Huguet

    The Journal of Mathematical Neuroscience 2013 3:13

    Published on: 14 August 2013

  6. Editorial

    Editorial for Special Issue on Neurodynamics

    “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...

    Stephen Coombes and Yulia Timofeeva

    The Journal of Mathematical Neuroscience 2013 3:10

    Published on: 14 August 2013