Journal ArticleDOI
Chaos via Shilnikov's Saddle-Node Bifurcation in a Theory of the Electroencephalogram
Reads0
Chats0
TLDR
It is shown that the chaos is spawned by a codimension-one homoclinic bifurcation that was analyzed by Shilnikov in 1969 but has never before been found in a physical application.Abstract:
We study the bifurcation diagram of a mesoscopic model of the human cortex. This model is known to exhibit robust chaotic behavior in the space of parameters that model exterior forcing. We show that the bifurcation diagram has an unusual degree of organization. In particular, we show that the chaos is spawned by a codimension-one homoclinic bifurcation that was analyzed by Shilnikov in 1969 but has never before been found in a physical application.read more
Citations
More filters
Journal ArticleDOI
Large-scale neural dynamics: simple and complex.
TL;DR: Extensions of the basic formalism to treat refractoriness, adaptive feedback and inhomogeneous connectivity are described along with open challenges for the development of multi-scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale.
Journal ArticleDOI
Bifurcation analysis of neural mass models: Impact of extrinsic inputs and dendritic time constants
TL;DR: This work systematically describes the oscillatory regimes which a NMM of a single cortical source with extrinsic input from other cortical and subcortical areas to each subpopulation can explain, using bifurcation analysis to describe qualitative changes in system behavior in response to quantitative input changes.
Journal ArticleDOI
Modeling brain resonance phenomena using a neural mass model.
Andreas Spiegler,Andreas Spiegler,Thomas R. Knösche,Karin Schwab,Jens Haueisen,Fatihcan M. Atay +5 more
TL;DR: The findings confirm that the NMM is a useful model of brain dynamics during photic driving and can be used to study the mechanisms of, for example, perception and epileptic seizure generation.
Journal ArticleDOI
A biophysical model of dynamic balancing of excitation and inhibition in fast oscillatory large-scale networks.
Romesh G. Abeysuriya,Jonathan Hadida,Stamatios N. Sotiropoulos,Stamatios N. Sotiropoulos,Stamatios N. Sotiropoulos,Saad Jbabdi,Robert Becker,Benjamin A. E. Hunt,Benjamin A. E. Hunt,Matthew J. Brookes,Mark W. Woolrich +10 more
TL;DR: This study simulates a cortical brain network using the Wilson-Cowan neural mass model with conduction delays and noise, and uses inhibitory synaptic plasticity (ISP) to dynamically achieve a spatially local balance between excitation and inhibition.
Journal ArticleDOI
The dynamic evolution of focal-onset epilepsies--combining theoretical and clinical observations.
Alex Blenkinsop,Antonio Valentin,Mark P. Richardson,John R. Terry,John R. Terry,John R. Terry +5 more
TL;DR: This study explored the relationship between model dynamics and clinical recordings from patients with focal epilepsies, and found that spikes in the considered model arose out of so‐called ‘false’ bifurcations, a finding consistent with other neural models with two timescales of inhibitory processes.
References
More filters
Book
Neocortical Dynamics and Human EEG Rhythms
TL;DR: This paper presents a meta-analyses of the statistical mechanics of multiple scales of neocortical interactions of Paul Nunez's "quantitative states of neocortex" and the "global contribution to EEG dynamics".
Journal ArticleDOI
Is there chaos in the brain? II. Experimental evidence and related models.
Henri Korn,Philippe Faure +1 more
TL;DR: The data and main arguments that support the existence of chaos at all levels from the simplest to the most complex forms of organization of the nervous system are presented.
Journal ArticleDOI
Waves, bumps, and patterns in neural field theories
TL;DR: This paper presents a review of neural field models of firing rate activity and shows how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons.
Related Papers (5)
Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons
Hugh R. Wilson,Jack D. Cowan +1 more