Collective almost synchronization-based model to extract and predict features of EEG signals.

Understanding the brain is important in the fields of science, medicine, and engineering. A promising approach to better understand the brain is through computing models. These models were adjusted to reproduce data collected from the brain. One of the most commonly used types of data in neuroscience comes from electroencephalography (EEG), which records the tiny voltages generated when neurons in the brain are activated. In this study, we propose a model based on complex networks of weakly connected dynamical systems (Hindmarsh-Rose neurons or Kuramoto oscillators), set to operate in a dynamic regime recognized as Collective Almost Synchronization (CAS). Our model not only successfully reproduces EEG data from both healthy and epileptic EEG signals, but it also predicts EEG features, the Hurst exponent, and the power spectrum. The proposed model is able to forecast EEG signals 5.76 s in the future. The average forecasting error was 9.22%. The random Kuramoto model produced the outstanding result for forecasting seizure EEG with an error of 11.21%.

Sound synchronization of bubble trains in a viscous fluid: experiment and modeling.

We investigate the dynamics of formation of air bubbles expelled from a nozzle immersed in a viscous fluid under the influence of sound waves. We have obtained bifurcation diagrams by measuring the time between successive bubbles, having the air flow (Q) as a parameter control for many values of the sound wave amplitude (A), the height (H) of the solution above the top of the nozzle, and three values of the sound frequency (fs). Our parameter spaces (Q,A) revealed a scenario for the onset of synchronization dominated by Arnold tongues (frequency locking) which gives place to chaotic phase synchronization for sufficiently large A. The experimental results were accurately reproduced by numerical simulations of a model combining a simple bubble growth model for the bubble train and a coupling term with the sound wave added to the equilibrium pressure.

Abundance of stable periodic behavior in a Red Grouse population model with delay: a consequence of homoclinicity.

Shrimp-shaped periodic regions embedded in chaotic regions in two-dimensional parameter spaces are of specific interest for physical and biological systems. We provide the first observation of these shrimp-shaped stability regions in a parameter space of a continuous time-delayed population model, obtained by taking the delays as bifurcation parameters. The parameter space organization is governed by the presence of infinitely many periodicity hubs, which trigger the spiraling organization of these shrimp-shaped periodic regions around them. We provide evidence that this spiraling organization in the parameter space is a consequence of the existence of homoclinic orbits in the phase space.