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  1. Content type: Research

    Neurons in a micro-circuit connected by chemical synapses can have their connectivity affected by the prior activity of the cells. The number of synapses available for releasing neurotransmitter can be decreas...

    Authors: Elham Bayat Mokhtari, J. Josh Lawrence and Emily F. Stone

    Citation: The Journal of Mathematical Neuroscience 2018 8:7

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  2. Content type: Research

    Many physiological phenomena have the property that some variables evolve much faster than others. For example, neuron models typically involve observable differences in time scales. The Hodgkin–Huxley model i...

    Authors: Cris R. Hasan, Bernd Krauskopf and Hinke M. Osinga

    Citation: The Journal of Mathematical Neuroscience 2018 8:5

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  3. Content type: Research

    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...

    Authors: Carlo R. Laing

    Citation: The Journal of Mathematical Neuroscience 2018 8:4

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  4. Content type: Research

    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...

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

    Citation: The Journal of Mathematical Neuroscience 2018 8:3

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  5. Content type: Research

    We investigate the sparse functional identification of complex cells and the decoding of spatio-temporal visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm is formulated as a ...

    Authors: Aurel A. Lazar, Nikul H. Ukani and Yiyin Zhou

    Citation: The Journal of Mathematical Neuroscience 2018 8:2

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  6. Content type: Research

    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...

    Authors: Christopher J. Hillar and Ngoc M. Tran

    Citation: The Journal of Mathematical Neuroscience 2018 8:1

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  7. Content type: Research

    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...

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

    Citation: The Journal of Mathematical Neuroscience 2017 7:13

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  8. Content type: Research

    Continuum neural field equations model the large-scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded a...

    Authors: Aytül Gökçe, Daniele Avitabile and Stephen Coombes

    Citation: The Journal of Mathematical Neuroscience 2017 7:12

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  9. Content type: Research

    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...

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

    Citation: The Journal of Mathematical Neuroscience 2017 7:10

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  10. Content type: Research

    Neural mass models provide a useful framework for modelling mesoscopic neural dynamics and in this article we consider the Jansen and Rit neural mass model (JR-NMM). We formulate a stochastic version of it whi...

    Authors: Markus Ableidinger, Evelyn Buckwar and Harald Hinterleitner

    Citation: The Journal of Mathematical Neuroscience 2017 7:8

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  11. Content type: Research

    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...

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

    Citation: The Journal of Mathematical Neuroscience 2017 7:7

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  12. Content type: Research

    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...

    Authors: Bjørn Fredrik Nielsen

    Citation: The Journal of Mathematical Neuroscience 2017 7:6

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  13. Content type: Research

    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, ...

    Authors: Arthur S. Sherman and Joon Ha

    Citation: The Journal of Mathematical Neuroscience 2017 7:4

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  14. Content type: Research

    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...

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

    Citation: The Journal of Mathematical Neuroscience 2017 7:2

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  15. Content type: Research

    Recent experimental evidence on the clustering of glutamate and GABA transporters on astrocytic processes surrounding synaptic terminals pose the question of the functional relevance of the astrocytes in the r...

    Authors: Aurélie Garnier, Alexandre Vidal and Habib Benali

    Citation: The Journal of Mathematical Neuroscience 2016 6:10

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  16. Content type: Research

    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...

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

    Citation: The Journal of Mathematical Neuroscience 2016 6:9

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  17. Content type: Research

    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...

    Authors: Bjørn Fredrik Nielsen and John Wyller

    Citation: The Journal of Mathematical Neuroscience 2016 6:7

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