Related papers: Codimension Two Bifurcations and Rythms in Neural …
Electrophysiological brain signals, such as electroencephalography (EEG), exhibit both periodic and aperiodic components, with the latter often modeled as 1/f noise and considered critical to cognitive and neurological processes. Although…
The electroencephalographic (EEG) data intracerebrally recorded from 20 epileptic humans with different brain origins of focal epilepsies or types of seizures, ages and sexes are investigated (nearly 700 million data). Multi channel…
The cascade-shell model of turbulence with six real variables originated by Gledzer is studied numerically using Mathematica 5.1. Periodic, doubly-periodic and chaotic solutions and the routes to chaos via both frequency-locking and…
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…
The Takens-Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation-invariant in one spatial dimension with no…
Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional…
The study and characterization of the diversity of spatiotemporal patterns generated when a rectangular layer of fluid is locally heated beneath its free surface is presented. We focus on the instability of a stationary cellular pattern of…
A method for the quantitative assessment of spatio-temporal structuring of brain activity is presented. This approach is employed in a longitudinal case study of a child with frontal lobe epilepsy (FLE) and tested against an age-matched…
We discuss the effect of noise on a system with a quasi-periodicity of different dimensions. As the basic model of our research we use the simplest three-dimensional map with two-frequency and three-frequency quasi-periodicity. Modification…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
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…
Recurrent Neural Network models have elucidated the interplay between structure and dynamics in biological neural networks, particularly the emergence of irregular and rhythmic activities in cortex. However, most studies have focused on…
We consider dynamical systems depending on one or more real parameters, and assuming that, for some ``critical'' value of the parameters, the eigenvalues of the linear part are resonant, we discuss the existence -- under suitable hypotheses…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
A codimension-three bifurcation, characterized by a pair of purely imaginary eigenvalues and a nonsemisimple double zero eigenvalue, arises in the study of a pair of weakly coupled nonlinear oscillators with Z_2 + Z_2 symmetry. The…
Epoch-wise double descent is the phenomenon where generalisation performance improves beyond the point of overfitting, resulting in a generalisation curve exhibiting two descents under the course of learning. Understanding the mechanisms…
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…
Epilepsy is a neurological disease characterized by recurrent and spontaneous seizures. It affects approximately 50 million people worldwide. In majority of the cases accurate diagnosis of the disease can be made without using any…
In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and its double Hopf bifurcations are investigated. The general post-bifurcation and stability analysis are carried out using the normal form of the…
Musical large-scale form is investigated using an Electronic Dance Music (EDM) piece fed into a Finite-Difference Time Domain (FDTD) physical model of the cochlear which again inputs into an Impulse-Pattern Formulation (IPF) brain model. In…