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Critical behaviour of the stochastic Wilson-Cowan model
- Source :
- PLoS Computational Biology, Vol 17, Iss 8, p e1008884 (2021), PLoS Computational Biology
- Publication Year :
- 2021
- Publisher :
- Public Library of Science (PLoS), 2021.
-
Abstract
- Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, 3/2 and 2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.<br />Author summary Networks of spiking neurons are introduced to describe some features of the brain activity, which are characterized by burst events (avalanches) with power-law distributions of size and duration. The observation of this kind of noisy behaviour in a wide variety of real systems led to the hypothesis that neuronal networks work in the proximity of a critical point. This hypothesis is at the core of an intense debate. At variance with previous claims, here we show that a stochastic version of the Wilson-Cowan model presents a phenomenology in agreement with the existence of a bona fide critical point for a particular choice of the relative synaptic weight between excitatory and inhibitory neurons. The system behaviour at this point shows all features typical of criticality, such as diverging timescales, scaling with the system size and scale-free distributions of avalanche sizes and durations, with exponents corresponding to the mean-field branching process. Our analysis unveils the critical nature of the observed behaviours.
- Subjects :
- Phase transition
Physiology
Social Sciences
Action Potentials
Parameter space
Critical point (thermodynamics)
Animal Cells
Relaxation Time
Psychology
Statistical physics
Biology (General)
Physics
Neurons
Ecology
Applied Mathematics
Simulation and Modeling
Brain
Electrophysiology
Computational Theory and Mathematics
Modeling and Simulation
Physical Sciences
Thermodynamics
Cellular Types
Algorithms
Neuronal Tuning
Research Article
Computer and Information Sciences
Neural Networks
QH301-705.5
Models, Neurological
Neurophysiology
Research and Analysis Methods
Membrane Potential
Cellular and Molecular Neuroscience
Synaptic weight
Spatio-Temporal Analysis
Genetics
Animals
Humans
Computer Simulation
Molecular Biology
Scaling
Relaxation (Physics)
Ecology, Evolution, Behavior and Systematics
Branching process
Behavior
Stochastic Processes
Quantitative Biology::Neurons and Cognition
Biology and Life Sciences
Computational Biology
Cell Biology
Renormalization group
Wilson–Cowan model
Electrophysiological Phenomena
Cellular Neuroscience
Linear Models
Linear approximation
Nerve Net
Mathematics
Neuroscience
Subjects
Details
- Language :
- English
- ISSN :
- 15537358
- Volume :
- 17
- Issue :
- 8
- Database :
- OpenAIRE
- Journal :
- PLoS Computational Biology
- Accession number :
- edsair.doi.dedup.....ef883cdf16d633cf60f589751d9668be