Related papers: Codimension Two Bifurcations and Rythms in Neural …
Identifying abnormal electroencephalographic activity is crucial in diagnosis and treatment of epilepsy. Recent studies showed that decomposing brain activity into periodic (oscillatory) and aperiodic (trend across all frequencies)…
A viscous thread falling from a nozzle onto a surface exhibits the famous rope-coiling effect, in which the thread buckles to form loops. If the surface is replaced by a belt moving with speed $U$, the rotational symmetry of the buckling…
This paper reports the first finding of cupolets in a chaotic Hindmarsh-Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme…
A novel flow state consisting of two oppositely travelling waves (TWs) with oscillating amplitudes has been found in the counterrotating Taylor-Couette system by full numerical simulations. This structure bifurcates out of axially standing…
Chimera states---the coexistence of synchrony and asynchrony in a nonlocally-coupled network of identical oscillators---are often used as a model framework for epileptic seizures. Here, we explore the dynamics of chimera states in a network…
The bifurcation and chaotic behaviour of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude ($a$) and frequency ($\omega$). A classification of the various types of bifurcations likely to…
Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting…
Epilepsy is a brain disorder due to abnormalactivity of neurons and recording of seizures is of primary interest in the evaluation of epileptic patients. A seizureis the phenomenon of rhythmicity discharge from either a local area or the…
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,…
Epileptic seizures are neurological disorders characterized by abnormal and excessive electrical activity in the brain, resulting in recurrent seizure events. Electroencephalogram (EEG) signals are widely used for seizure diagnosis due to…
Through multiple-scales and symmetry arguments we derive a model set of amplitude equations describing the interaction of two steady-state pattern-forming instabilities, in the case that the wavelengths of the instabilities are nearly in…
Electroencephalography (EEG) monitors ---by either intrusive or noninvasive electrodes--- time and frequency variations and spectral content of voltage fluctuations or waves, known as brain rhythms, which in some way uncover activity during…
The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I…
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…
Nonlinear time series analyses have suggested that the human electroencephalogram (EEG) may share statistical and dynamical properties with chaotic systems. During slow-wave sleep or pathological states like epilepsy, correlation dimension…
We use perturbation theory and bifurcation theory to analyze the dynamical behavior of resonances, associated to a model describing a particle moving within a ring around a celestial object. The central body is modeled as a homogeneous…
A brain wide association study (BWAS) based on the logistic regression was first developed and applied to a large population of epilepsy patients (168) and healthy controls (136). It was found that the most significant links associated with…
Background and Objectives: Many biological processes are modulated by rhythms on circadian and multidien timescales. In focal epilepsy, various seizure features, such as spread and duration, can change from one seizure to the next within…
We study the complex nonlinear dynamics of the two-photon Dicke model in the semiclassical limit by considering cavity and qubit dissipation. In addition to the normal and super-radiant phases, another phase that contains abundant…
Epilepsy, affecting approximately 50 million people globally, is characterized by abnormal brain activity and remains challenging to treat. The diagnosis of epilepsy relies heavily on electroencephalogram (EEG) data, where specialists…