Additive noise quenches delay-induced oscillations

Noise has significant impact on nonlinear phenomena. Here we demonstrate that, in opposition to previous assumptions, additive noise interfere with the linear stability of scalar nonlinear systems when these are subject to time delay. We show this by performing a recently designed time-dependent delayed center manifold (DCM) reduction around an Hopf bifurcation in a model of nonlinear negative feedback. Using this, we show that noise intensity must be considered as a bifurcation parameter and thus shifts the threshold at which emerge delay-induced rhythmic solutions.Comment: pre-print submitted versio

Detection of transient generalized and mutual phase synchronization by clustering and application by single brain signals

The present work introduces an analysis framework for the detection of metastable signal segments in multivariate time series. It is shown that in case of linear data these segments represent transient generalized synchronization, while metastable segments in circular data reflect transient mutual phase synchronization. We propose a single segmentation approach for both types of data considering the space-time structure of the data. Applications to both event-related potentials and single evoked potentials obtained from an auditory oddball experiment reveal the lack of the component P300 in an experimental condition, indicates attention effects in component N100 and shows dramatic latency jitters in single trials. A comparison of the proposed method to a conventional index of mutual phase synchronization demonstrates the superiority of considering space-time data structures

External stimulation induces switches between neural oscillations: an illustrative feedback model

International audienc

Stability and bifurcations in neural fields with axonal delay and general connectivity

A stability analysis is presented for neural field equations in the presence of axonal delays and for a general class of connectivity kernels and synaptic properties. Sufficient conditions are given for the stability of equilibrium solutions. It is shown that the delays play a crucial role in non-stationary bifurcations of equilibria, whereas the stationary bifurcations depend only on the kernel. Bounds are determined for the frequencies of bifurcating periodic solutions. A perturbative scheme is used to calculate the types of bifurcations leading to spatial patterns, oscillatory solutions, and traveling waves. For high transmission speeds a simple method is derived that allows the determination of the bifurcation type by visual inspection of the Fourier transforms of the connectivity kernel and its first moment. Results are numerically illustrated on a class of neurologically plausible second order systems with combinations of Gaussian excitatory and inhibitory connections

Brain connectivity reduction reflects disturbed self-organisation of the brain: Neural disorders and General Anesthesia

International audienceThe neurophysiological correlate of functional neural impairment is an open problem. Functional impairment may be observed as mental disorder, seizures or modification of consciousness level. The latter include loss of responsiveness under general anaesthesia, sleep or even trance in hypnosis. This chapter points out the relation between reduced brain connectivity as a possible correlate of neural functional impairment and self-organisation in the brain. A first numerical example demonstrates how neural noise disturbs self-organisation in the brain. Estimators of self-organisation such as global phase synchrony or information transfer quantify the degree of self-organisation. The chapter shows up by a brief literature review how these estimators indicate brain connectivity modifications in neural disorders and under general anaesthesia

Improvement of source localization by dynamical systems based modelling

Summary: Recently, we have proposed a new concept for analyzing EEG/MEG data (Uhl et al. 1998), which leads to a dynamical systems based modeling (DSBM) of neurophysiological data. We report the application of this approach to four different classes of simulated noisy data sets, to investigate the impact of DSBM-filtering on source localization. An improvement is demonstrated of up to above 50 % of the distance between simulated and estimated dipole positions compared to principal component filtered and unfiltered data. On a noise level on which two underlying dipoles cannot be resolved from the unfiltered data, DSBM allows for an extraction of the two sources

Forecast of Spectral Features by Ensemble Data Assimilation

Data assimilation permits to compute optimal forecasts in high-dimensional systems as, e.g., in weather forecasting. Typically such forecasts are spatially distributed time series of system variables. We hypothesize that such forecasts are not optimal if the major interest does not lie in the temporal evolution of system variables but in time series composites or features. For instance, in neuroscience spectral features of neural activity are the primary functional elements. The present work proposes a data assimilation framework for forecasts of time-frequency distributions. The framework comprises the ensemble Kalman filter and a detailed statistical ensemble verification. The performance of the framework is evaluated for a simulated FitzHugh-Nagumo model, various measurement noise levels and for in situ-, nonlocal and speed observations. We discover a resonance effect in forecast errors between forecast time and frequencies in observations