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  1. Research

    The Dynamics of Networks of Identical Theta Neurons

    We consider finite and infinite all-to-all coupled networks of identical theta neurons. Two types of synaptic interactions are investigated: instantaneous and delayed (via first-order synaptic processing). Ext...

    Carlo R. Laing

    The Journal of Mathematical Neuroscience 2018 8:4

    Published on: 5 February 2018

  2. Research

    Kernel Reconstruction for Delayed Neural Field Equations

    Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with conside...

    Jehan Alswaihli, Roland Potthast, Ingo Bojak, Douglas Saddy and Axel Hutt

    The Journal of Mathematical Neuroscience 2018 8:3

    Published on: 5 February 2018

  3. Research

    Robust Exponential Memory in Hopfield Networks

    The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically coupled McCulloch–Pitts binary neurons interact to perform emergent computation. Alt...

    Christopher J. Hillar and Ngoc M. Tran

    The Journal of Mathematical Neuroscience 2018 8:1

    Published on: 16 January 2018

  4. Research

    A Rate-Reduced Neuron Model for Complex Spiking Behavior

    We present a simple rate-reduced neuron model that captures a wide range of complex, biologically plausible, and physiologically relevant spiking behavior. This includes spike-frequency adaptation, postinhibit...

    Koen Dijkstra, Yuri A. Kuznetsov, Michel J. A. M. van Putten and Stephan A. van Gils

    The Journal of Mathematical Neuroscience 2017 7:13

    Published on: 11 December 2017

  5. Research

    Symmetries Constrain Dynamics in a Family of Balanced Neural Networks

    We examine a family of random firing-rate neural networks in which we enforce the neurobiological constraint of Dale’s Law—each neuron makes either excitatory or inhibitory connections onto its post-synaptic t...

    Andrea K. Barreiro, J. Nathan Kutz and Eli Shlizerman

    The Journal of Mathematical Neuroscience 2017 7:10

    Published on: 10 October 2017

  6. Research

    Fast–Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-slow Transitions of Classes

    Bursting is a phenomenon found in a variety of physical and biological systems. For example, in neuroscience, bursting is believed to play a key role in the way information is transferred in the nervous system...

    Maria Luisa Saggio, Andreas Spiegler, Christophe Bernard and Viktor K. Jirsa

    The Journal of Mathematical Neuroscience 2017 7:7

    Published on: 25 July 2017

  7. Research

    Regularization of Ill-Posed Point Neuron Models

    Point neuron models with a Heaviside firing rate function can be ill-posed. That is, the initial-condition-to-solution map might become discontinuous in finite time. If a Lipschitz continuous but steep firing rat...

    Bjørn Fredrik Nielsen

    The Journal of Mathematical Neuroscience 2017 7:6

    Published on: 14 July 2017

  8. Research

    How Adaptation Makes Low Firing Rates Robust

    Low frequency firing is modeled by Type 1 neurons with a SNIC, but, because of the vertical slope of the square-root-like fI curve, low f only occurs over a narrow range of I. When an adaptive current is added, ...

    Arthur S. Sherman and Joon Ha

    The Journal of Mathematical Neuroscience 2017 7:4

    Published on: 24 June 2017

  9. Research

    Emergent Dynamical Properties of the BCM Learning Rule

    The Bienenstock–Cooper–Munro (BCM) learning rule provides a simple setup for synaptic modification that combines a Hebbian product rule with a homeostatic mechanism that keeps the weights bounded. The homeosta...

    Lawrence C. Udeigwe, Paul W. Munro and G. Bard Ermentrout

    The Journal of Mathematical Neuroscience 2017 7:2

    Published on: 20 February 2017

  10. Research

    Analytic Modeling of Neural Tissue: I. A Spherical Bidomain

    Presented here is a model of neural tissue in a conductive medium stimulated by externally injected currents. The tissue is described as a conductively isotropic bidomain, i.e. comprised of intra and extracell...

    Benjamin L. Schwartz, Munish Chauhan and Rosalind J. Sadleir

    The Journal of Mathematical Neuroscience 2016 6:9

    Published on: 9 September 2016

  11. Research

    Ill-Posed Point Neuron Models

    We show that point-neuron models with a Heaviside firing rate function can be ill posed. More specifically, the initial-condition-to-solution map might become discontinuous in finite time. Consequently, if finite...

    Bjørn Fredrik Nielsen and John Wyller

    The Journal of Mathematical Neuroscience 2016 6:7

    Published on: 30 April 2016

  12. Research

    Entrainment Ranges for Chains of Forced Neural and Phase Oscillators

    Sensory input to the lamprey central pattern generator (CPG) for locomotion is known to have a significant role in modulating lamprey swimming. Lamprey CPGs are known to have the ability to entrain to a bendin...

    Nicole Massarelli, Geoffrey Clapp, Kathleen Hoffman and Tim Kiemel

    The Journal of Mathematical Neuroscience 2016 6:6

    Published on: 18 April 2016

  13. Research

    Wave Generation in Unidirectional Chains of Idealized Neural Oscillators

    We investigate the dynamics of unidirectional semi-infinite chains of type-I oscillators that are periodically forced at their root node, as an archetype of wave generation in neural networks. In previous stud...

    Bastien Fernandez and Stanislav M. Mintchev

    The Journal of Mathematical Neuroscience 2016 6:5

    Published on: 8 April 2016

  14. Research

    Neural Field Models with Threshold Noise

    The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the class...

    Rüdiger Thul, Stephen Coombes and Carlo R. Laing

    The Journal of Mathematical Neuroscience 2016 6:3

    Published on: 2 March 2016

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