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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...
The Journal of Mathematical Neuroscience 2017 7:7
Published on: 25 July 2017
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...
The Journal of Mathematical Neuroscience 2017 7:6
Published on: 14 July 2017
Research
Neural field equations are used to describe the spatio-temporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves...
The Journal of Mathematical Neuroscience 2017 7:5
Published on: 6 July 2017
Research
Low frequency firing is modeled by Type 1 neurons with a SNIC, but, because of the vertical slope of the square-root-like f–I curve, low f only occurs over a narrow range of I. When an adaptive current is added, ...
The Journal of Mathematical Neuroscience 2017 7:4
Published on: 24 June 2017
Research
Neural networks generate a variety of rhythmic activity patterns, often involving different timescales. One example arises in the respiratory network in the pre-Bötzinger complex of the mammalian brainstem, wh...
The Journal of Mathematical Neuroscience 2017 7:3
Published on: 6 June 2017
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...
The Journal of Mathematical Neuroscience 2017 7:2
Published on: 20 February 2017
Research
Homeostatic processes that provide negative feedback to regulate neuronal firing rates are essential for normal brain function. Indeed, multiple parameters of individual neurons, including the scale of afferen...
The Journal of Mathematical Neuroscience 2017 7:1
Published on: 17 January 2017
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...
The Journal of Mathematical Neuroscience 2016 6:10
Published on: 21 December 2016
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...
The Journal of Mathematical Neuroscience 2016 6:9
Published on: 9 September 2016
Research
A fundamental question concerning the way the visual world is represented in our brain is how a cortical cell responds when its classical receptive field contains a plurality of stimuli. Two opposing models ha...
The Journal of Mathematical Neuroscience 2016 6:8
Published on: 23 May 2016
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...
The Journal of Mathematical Neuroscience 2016 6:7
Published on: 30 April 2016
Research
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...
The Journal of Mathematical Neuroscience 2016 6:6
Published on: 18 April 2016
Research
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...
The Journal of Mathematical Neuroscience 2016 6:5
Published on: 8 April 2016
Editorial
Jack Cowan’s remarkable career has spanned, and molded, the development of neuroscience as a quantitative and mathematical discipline combining deep theoretical contributions, rigorous mathematical work and gr...
The Journal of Mathematical Neuroscience 2016 6:4
Published on: 4 April 2016
Research
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...
The Journal of Mathematical Neuroscience 2016 6:3
Published on: 2 March 2016
Review
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to s...
The Journal of Mathematical Neuroscience 2016 6:2
Published on: 6 January 2016
Research
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...
The Journal of Mathematical Neuroscience 2016 6:1
Published on: 4 January 2016
Research
With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus ...
The Journal of Mathematical Neuroscience (JMN) 2015 5:20
Published on: 5 October 2015
Research
The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. We have developed an understanding of the circuit mechanisms that lead to...
The Journal of Mathematical Neuroscience (JMN) 2015 5:17
Published on: 1 September 2015
Short report
In this note, we clarify the well-posedness of the limit equations to the mean-field N-neuron models proposed in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos...
The Journal of Mathematical Neuroscience (JMN) 2015 5:19
Published on: 1 September 2015
Short report
In a previous work (Dafilis et al. in Chaos 23(2):023111, 2013), evidence was presented for four-dimensional chaos in Liley’s mesoscopic model of the electroencephalogram. The study was limited to one paramete...
The Journal of Mathematical Neuroscience (JMN) 2015 5:18
Published on: 12 August 2015
Research
We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define e...
The Journal of Mathematical Neuroscience (JMN) 2015 5:16
Published on: 6 August 2015
Research
Rhythmic behaviors such as breathing, walking, and scratching are vital to many species. Such behaviors can emerge from groups of neurons, called central pattern generators, in the absence of rhythmic inputs. ...
The Journal of Mathematical Neuroscience (JMN) 2015 5:15
Published on: 17 July 2015
Research
The concept of cell assembly was introduced by Hebb and formalized mathematically by Palm in the framework of graph theory. In the study of associative memory, a cell assembly is a group of neurons that are st...
The Journal of Mathematical Neuroscience (JMN) 2015 5:14
Published on: 14 July 2015
Research
Simple-spike synchrony between Purkinje cells projecting to a common neuron in the deep cerebellar nucleus is emerging as an important factor in the encoding of output information from cerebellar cortex. A phe...
The Journal of Mathematical Neuroscience (JMN) 2015 5:13
Published on: 19 June 2015
