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  1. Hugh Wilson has proposed a class of models that treat higher-level decision making as a competition between patterns coded as levels of a set of attributes in an appropriately defined network (Cortical Mechani...

    Authors: Casey O Diekman and Martin Golubitsky

    Citation: The Journal of Mathematical Neuroscience 2014 4:12

    Content type: Research

    Published on:

  2. We study the effects of synaptic plasticity on the determination of firing period and relative phases in a network of two oscillatory neurons coupled with reciprocal inhibition. We combine the phase response c...

    Authors: Zeynep Akcay, Amitabha Bose and Farzan Nadim

    Citation: The Journal of Mathematical Neuroscience 2014 4:8

    Content type: Research

    Published on:

  3. The most basic functional role commonly ascribed to synchrony in the brain is that of amplifying excitatory neuronal signals. The reasoning is straightforward: When positive charge is injected into a leaky tar...

    Authors: Christoph Börgers, Jie Li and Nancy Kopell

    Citation: The Journal of Mathematical Neuroscience 2014 4:10

    Content type: Research

    Published on:

  4. The observation of apparent power laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of sel...

    Authors: Caroline Hartley, Timothy J Taylor, Istvan Z Kiss, Simon F Farmer and Luc Berthouze

    Citation: The Journal of Mathematical Neuroscience 2014 4:9

    Content type: Research

    Published on:

  5. Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochast...

    Authors: Deena R Schmidt and Peter J Thomas

    Citation: The Journal of Mathematical Neuroscience 2014 4:6

    Content type: Research

    Published on:

  6. We propose a theoretical motivation to quantify actual physiological features, such as the shape index distributions measured by Jones and Palmer in cats and by Ringach in macaque monkeys. We will adopt the un...

    Authors: D Barbieri, G Citti and A Sarti

    Citation: The Journal of Mathematical Neuroscience 2014 4:5

    Content type: Research

    Published on:

  7. Analysis of sinusoidal noisy leaky integrate-and-fire models and comparison with experimental data are important to understand the neural code and neural synchronization and rhythms. In this paper, we propose ...

    Authors: Alexandre Iolov, Susanne Ditlevsen and André Longtin

    Citation: The Journal of Mathematical Neuroscience 2014 4:4

    Content type: Research

    Published on:

  8. When dealing with classical spike train analysis, the practitioner often performs goodness-of-fit tests to test whether the observed process is a Poisson process, for instance, or if it obeys another type of p...

    Authors: Patricia Reynaud-Bouret, Vincent Rivoirard, Franck Grammont and Christine Tuleau-Malot

    Citation: The Journal of Mathematical Neuroscience 2014 4:3

    Content type: Research

    Published on:

  9. Population density models that are used to describe the evolution of neural populations in a phase space are closely related to the single neuron model that describes the individual trajectories of the neurons...

    Authors: Grégory Dumont, Jacques Henry and Carmen Oana Tarniceriu

    Citation: The Journal of Mathematical Neuroscience 2014 4:2

    Content type: Research

    Published on:

  10. We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape....

    Authors: Christian Kuehn and Martin G Riedler

    Citation: The Journal of Mathematical Neuroscience 2014 4:1

    Content type: Research

    Published on:

  11. 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

    Content type: Research

    Published on:

  12. 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

    Content type: Research

    Published on:

  13. 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

    Content type: Research

    Published on:

  14. 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

    Content type: Research

    Published on:

  15. “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

    Content type: Editorial

    Published on:

  16. The spread of activity in neural populations is a well-known phenomenon. To understand the propagation speed and the stability of stationary fronts in neural populations, the present work considers a neural fi...

    Authors: Axel Hutt and Linghai Zhang

    Citation: The Journal of Mathematical Neuroscience 2013 3:9

    Content type: Research

    Published on:

  17. Theoretical models of associative memory generally assume most of their parameters to be homogeneous across the network. Conversely, biological neural networks exhibit high variability of structural as well as...

    Authors: Daniel Medina and Christian Leibold

    Citation: The Journal of Mathematical Neuroscience 2013 3:8

    Content type: Research

    Published on:

  18. Binocular rivalry is the alternation in visual perception that can occur when the two eyes are presented with different images. Wilson proposed a class of neuronal network models that generalize rivalry to mul...

    Authors: Casey O Diekman, Martin Golubitsky and Yunjiao Wang

    Citation: The Journal of Mathematical Neuroscience 2013 3:6

    Content type: Research

    Published on:

  19. In this paper, we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate ...

    Authors: Timothy J Taylor, Caroline Hartley, Péter L Simon, Istvan Z Kiss and Luc Berthouze

    Citation: The Journal of Mathematical Neuroscience 2013 3:5

    Content type: Research

    Published on:

  20. Mathematical neuroendocrinology is a branch of mathematical neurosciences that is specifically interested in endocrine neurons, which have the uncommon ability of secreting neurohormones into the blood. One of...

    Authors: Maciej Krupa, Alexandre Vidal and Frédérique Clément

    Citation: The Journal of Mathematical Neuroscience 2013 3:4

    Content type: Research

    Published on:

  21. Although spike trains are the principal channel of communication between neurons, a single stimulus will elicit different spike trains from trial to trial. This variability, in both spike timings and spike num...

    Authors: Hannah Julienne and Conor Houghton

    Citation: The Journal of Mathematical Neuroscience 2013 3:3

    Content type: Research

    Published on:

  22. Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to wea...

    Authors: Kyle CA Wedgwood, Kevin K Lin, Ruediger Thul and Stephen Coombes

    Citation: The Journal of Mathematical Neuroscience 2013 3:2

    Content type: Research

    Published on:

  23. We analytically investigate the stability of splay states in the networks of N globally pulse-coupled phase-like models of neurons. We develop a perturbative technique which allows determining the Floquet exponen...

    Authors: Simona Olmi, Antonio Politi and Alessandro Torcini

    Citation: The Journal of Mathematical Neuroscience 2012 2:12

    Content type: Research

    Published on:

  24. Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties ...

    Authors: Quentin Caudron, Simon R Donnelly, Samuel PC Brand and Yulia Timofeeva

    Citation: The Journal of Mathematical Neuroscience 2012 2:11

    Content type: Research

    Published on:

  25. We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are repre...

    Authors: Javier Baladron, Diego Fasoli, Olivier Faugeras and Jonathan Touboul

    Citation: The Journal of Mathematical Neuroscience 2012 2:10

    Content type: Research

    Published on:

  26. Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where ...

    Authors: Stephen Coombes, Helmut Schmidt and Ingo Bojak

    Citation: The Journal of Mathematical Neuroscience 2012 2:9

    Content type: Research

    Published on:

  27. A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considere...

    Authors: Sid Visser, Hil GE Meijer, Michel JAM van Putten and Stephan A van Gils

    Citation: The Journal of Mathematical Neuroscience 2012 2:8

    Content type: Research

    Published on:

  28. In this paper, we analyze the invasion and extinction of activity in heterogeneous neural fields. We first consider the effects of spatial heterogeneities on the propagation of an invasive activity front. In c...

    Authors: Paul C Bressloff

    Citation: The Journal of Mathematical Neuroscience 2012 2:6

    Content type: Research

    Published on:

  29. We consider a coupled, heterogeneous population of relaxation oscillators used to model rhythmic oscillations in the pre-Bötzinger complex. By choosing specific values of the parameter used to describe the het...

    Authors: Carlo R Laing, Yu Zou, Ben Smith and Ioannis G Kevrekidis

    Citation: The Journal of Mathematical Neuroscience 2012 2:5

    Content type: Research

    Published on:

  30. Rapid action potential generation - spiking - and alternating intervals of spiking and quiescence - bursting - are two dynamic patterns commonly observed in neuronal activity. In computational models of neuron...

    Authors: John Burke, Mathieu Desroches, Anna M Barry, Tasso J Kaper and Mark A Kramer

    Citation: The Journal of Mathematical Neuroscience 2012 2:3

    Content type: Research

    Published on:

  31. We study synaptic plasticity in a complex neuronal cell model where NMDA-spikes can arise in certain dendritic zones. In the context of reinforcement learning, two kinds of plasticity rules are derived, zone r...

    Authors: Mathieu Schiess, Robert Urbanczik and Walter Senn

    Citation: The Journal of Mathematical Neuroscience 2012 2:2

    Content type: Research

    Published on:

  32. We describe a phenomenological model of seizure initiation, consisting of a bistable switch between stable fixed point and stable limit-cycle attractors. We determine a quasi-analytic formula for the exit time...

    Authors: Oscar Benjamin, Thomas HB Fitzgerald, Peter Ashwin, Krasimira Tsaneva-Atanasova, Fahmida Chowdhury, Mark P Richardson and John R Terry

    Citation: The Journal of Mathematical Neuroscience 2012 2:1

    Content type: Research

    Published on:

  33. We introduce a test for robustness of heteroclinic cycles that appear in neural microcircuits modeled as coupled dynamical cells. Robust heteroclinic cycles (RHCs) can appear as robust attractors in Lotka-Volt...

    Authors: Peter Ashwin, Özkan Karabacak and Thomas Nowotny

    Citation: The Journal of Mathematical Neuroscience 2011 1:13

    Content type: Research

    Published on:

  34. Pituitary cells of the anterior pituitary gland secrete hormones in response to patterns of electrical activity. Several types of pituitary cells produce short bursts of electrical activity which are more effe...

    Authors: Wondimu Teka, Joël Tabak, Theodore Vo, Martin Wechselberger and Richard Bertram

    Citation: The Journal of Mathematical Neuroscience 2011 1:12

    Content type: Research

    Published on:

  35. We employ a Hodgkin-Huxley-type model of basolateral ionic currents in bullfrog saccular hair cells for studying the genesis of spontaneous voltage oscillations and their role in shaping the response of the ha...

    Authors: Alexander B Neiman, Kai Dierkes, Benjamin Lindner, Lijuan Han and Andrey L Shilnikov

    Citation: The Journal of Mathematical Neuroscience 2011 1:11

    Content type: Research

    Published on:

  36. Dendritic spines are small protrusions on a neuronal dendrite that are the main locus of excitatory synaptic connections. Although their geometry is variable over time and along the dendrite, they typically co...

    Authors: David Holcman and Zeev Schuss

    Citation: The Journal of Mathematical Neuroscience 2011 1:10

    Content type: Research

    Published on:

  37. A major obstacle in the analysis of many physiological models is the issue of model simplification. Various methods have been used for simplifying such models, with one common technique being to eliminate cert...

    Authors: Wenjun Zhang, Vivien Kirk, James Sneyd and Martin Wechselberger

    Citation: The Journal of Mathematical Neuroscience 2011 1:9

    Content type: Research

    Published on:

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