Related papers: Understanding Epileptiform After-Discharges as Rhy…
In this paper, an attempt has been made to understand the parametric excitation of a periodic orbit of nonlinear oscillator which can be a limit cycle, center or a slowly decaying center-type oscillation. For this a delay model is…
We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical…
Functional connectivity is a fundamental property of neural networks that quantifies the segregation and integration of information between cortical areas. Due to mathematical complexity, a theory that could explain how the parameters of…
In various neurological disorders spatio-temporal excitation patterns constitute examples of excitable behavior emerging from pathological pathways. During migraine, seizure, and stroke an initially localized pathological state can…
High frequency oscillations (HFOs) are a promising biomarker of epileptic brain tissue and activity. HFOs additionally serve as a prototypical example of challenges in the analysis of discrete events in high-temporal resolution,…
The stability and bifurcation behaviour of a wake-induced vibro-impacting oscillator is studied. The effects of a discontinuity on the stability of the structure while it is undergoing phase-locked motions due to the surrounding…
EEG slowing is reported in various neurological disorders including Alzheimer's, Parkinson's and Epilepsy. Here, we investigate alpha rhythm slowing in individuals with refractory temporal lobe epilepsy (TLE), compared to healthy controls,…
Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of…
To define the neural networks responsible of the epileptic seizure, we had to study the electrophysiological signal in a proper way. The early recognition of the seizure build up could also be defined through the time space mapping of the…
We consider the electrical signals recorded from a subdural array of electrodes placed on the pial surface of the brain for chronic evaluation of epileptic patients before surgical resection. A simple and computationally fast method to…
Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable…
The brain can be understood as a collection of interacting neuronal oscillators, but the extent to which its sustained activity is due to coupling among brain areas is still unclear. Here we study the joint dynamics of two cortical columns…
Brain oscillations exhibit long-range temporal correlations (LRTCs), which reflect the regularity of their fluctuations: low values representing more random (decorrelated) while high values more persistent (correlated) dynamics. LRTCs…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of…
We use a computational model to propose a physiological mechanism by which transient control of beta oscillations in the indirect pathway of the basal ganglia is orchestrated at the cellular level. Our model includes a simple and robust…
The neural oscillator model proposed by Matsuoka is a piecewise affine system, which exhibits distinctive periodic solutions. Although such typical oscillation patterns have been widely studied, little is understood about the dynamics of…
Neural computation is associated with the emergence, reconfiguration and dissolution of cell assemblies in the context of varying oscillatory states. Here, we describe the complex spatio-temporal dynamics of cell assemblies through temporal…
The epileptic mechanism is postulated as that an animal's neurons gradually diminish their inhibition function coupled with enhanced excitation when an epileptic event is approaching. Calcium imaging technique is designed to directly record…
We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of…