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Stochastic Network Models in Neuroscience

  1. Research

    Wilson–Cowan Equations for Neocortical Dynamics

    In 1972–1973 Wilson and Cowan introduced a mathematical model of the population dynamics of synaptically coupled excitatory and inhibitory neurons in the neocortex. The model dealt only with the mean numbers o...

    Jack D. Cowan, Jeremy Neuman and Wim van Drongelen

    The Journal of Mathematical Neuroscience 2016 6:1

    Published on: 4 January 2016

  2. Research

    Noise-Induced Precursors of State Transitions in the Stochastic Wilson–Cowan Model

    The Wilson–Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here ...

    Ehsan Negahbani, D. Alistair Steyn-Ross, Moira L. Steyn-Ross, Marcus T. Wilson and Jamie W. Sleigh

    The Journal of Mathematical Neuroscience (JMN) 2015 5:9

    Published on: 8 April 2015

  3. Research

    Modeling Focal Epileptic Activity in the Wilson–Cowan Model with Depolarization Block

    Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity...

    Hil G. E. Meijer, Tahra L. Eissa, Bert Kiewiet, Jeremy F. Neuman, Catherine A. Schevon, Ronald G. Emerson, Robert R. Goodman, Guy M. McKhann Jr., Charles J. Marcuccilli, Andrew K. Tryba, Jack D. Cowan, Stephan A. van Gils and Wim van Drongelen

    The Journal of Mathematical Neuroscience (JMN) 2015 5:7

    Published on: 27 March 2015

  4. Research

    Path Integral Methods for Stochastic Differential Equations

    Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic...

    Carson C. Chow and Michael A. Buice

    The Journal of Mathematical Neuroscience (JMN) 2015 5:8

    Published on: 24 March 2015