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We study a simple map as a minimal model of excitable cells. The map has two fast variables which mimic the behavior of class I neurons, undergoing a sub-critical Hopf bifurcation. Adding a third slow variable allows the system to present…
Synchronous oscillations of neuronal populations support resting-state cortical activity. Recent studies indicate that resting-state functional connectivity is not static, but exhibits complex dynamics. The mechanisms underlying the complex…
Focal seizures are episodes of pathological brain activity that appear to arise from a localised area of the brain. The onset patterns of focal seizure activity have been studied intensively, and they have largely been distinguished into…
The neuronal circuit that controls obsessive and compulsive behaviors involves a complex network of brain regions (some with known involvement in reward processing). Among these are cortical regions, the striatum and the thalamus (which…
Oscillatory activities are widely observed in specific frequency bands of recorded field potentials in different brain regions, and play critical roles in processing neural information. Understanding the structure of these oscillatory…
Localized persistent cortical neural activity is a validated neural substrate of parametric working memory. Such activity `bumps' represent the continuous location of a cue over several seconds. Pyramidal (excitatory) and interneuronal…
Neuronal correlates of Parkinson's disease (PD) include a slowing of the electroencephalogram (EEG) and enhanced synchrony at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a physiologically…
Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…
In neurosciences, the brain processes information via the firing patterns of connected neurons operating across a spectrum of frequencies. To better understand the effects of these frequencies in the neuron dynamics, we have simulated a…
There is growing evidence in favour of the temporal-coding hypothesis that temporal correlation of neuronal discharges may serve to bind distributed neuronal activity into unique representations and, in particular, that $\theta$ (3.5-7.5…
Broadband spontaneous macroscopic neural oscillations are rhythmic cortical firing which were extensively examined during the last century, however, their possible origination is still controversial. In this work we show how macroscopic…
Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have…
We examine the effects of stochastic input currents on the firing behavior of two excitable neurons coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling…
We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…
We report a noise induced delay of bifurcation in a simple pulse-coupled neural circuit. We study the behavior of two neural oscillators, each individually governed by saddle-node dynamics, with reciprocal excitatory synaptic connections.…
We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with…
A number of experiments have evidenced signatures of enhanced superconducting correlations after photoexcitation. Initially, these experiments were interpreted as resulting from quasi-static changes in the Hamiltonian parameters, for…
Changes in brain states, as found in many neurological diseases such as epilepsy, are often described as bifurcations in mesoscopic neural models. Nearly all of these models rely on a mathematically convenient, but biophysically inaccurate,…
Neuronal excitability is known to be affected by transcranial electrical stimulation. However, due to the existence of both excitatory and inhibitory neurons in the cortex, the mechanism of neuronal excitability shift is still not clear.…
Transient and equilibrium synchronizations in complex neuronal networks as a consequence of dynamics induced by having sources placed at specific neurons are investigated. The basic integrate-and-fire neuron is adopted, and the dynamics is…