scholarly journals Dynamics of Populations of Integrate-and-Fire Neurons, Partial Synchronization and Memory

1993 ◽  
Vol 5 (4) ◽  
pp. 570-586 ◽  
Author(s):  
Marius Usher ◽  
Heinz Georg Schuster ◽  
Ernst Niebur
Keyword(s):  
Functional Role ◽  
Temporal Dynamics ◽  
Mean Field ◽  
External Input ◽  
Field Potentials ◽  
Field Approach ◽  
Integrate And Fire ◽  
Delay Times ◽  
Dynamics Of Populations ◽  
Global Activity

We study the dynamics of completely connected populations of refractory integrate-and-fire neurons in the presence of noise. Solving the master equation based on a mean-field approach, and by computer simulations, we find sustained states of activity that correspond to fixed points and show that for the same value of external input, the system has one or two attractors. The dynamic behavior of the population under the influence of external input and noise manifests hysteresis effects that might have a functional role for memory. The temporal dynamics at higher temporal resolution, finer than the transmission delay times and the refractory period, are characterized by synchronized activity of subpopulations. The global activity of the population shows aperiodic oscillations analogous to experimentally found field potentials.

scholarly journals Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates

1999 ◽  
Vol 11 (7) ◽  
pp. 1621-1671 ◽  
Author(s):  
Nicolas Brunel ◽  
Vincent Hakim
Keyword(s):  
Coherence Time ◽  
External Input ◽  
Sharp Transition ◽  
Firing Rates ◽  
Integrate And Fire ◽  
Global Oscillation ◽  
Inhibitory Feedback ◽  
Low Rate ◽  
Global Activity ◽  
Good Agreement

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N → ∞, the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters in these two different regimes. The results are found to be in good agreement with numerical simulations.

scholarly journals A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models

2019 ◽  
Author(s):  
M. Carlu ◽  
O. Chehab ◽  
L. Dalla Porta ◽  
D. Depannemaecker ◽  
C. Héricé ◽  
...  
Keyword(s):  
Temporal Dynamics ◽  
Mean Field ◽  
Population Models ◽  
Inhibitory Neurons ◽  
Mathematical Tool ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
Mean Field Models ◽  
Electrophysiological Recordings ◽  
Field Formalism

AbstractWe present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the populations response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHYPopulation models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

scholarly journals Stochastic dynamics and mean field approach in a system of three interacting species

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Davide Valenti ◽  
Bernardo Spagnolo
Keyword(s):  
Stochastic Dynamics ◽  
Temporal Dynamics ◽  
Mean Field ◽  
Spatial Domain ◽  
Volterra Equations ◽  
Time Behaviour ◽  
Time Step ◽  
Field Approach ◽  
Interacting Species ◽  
Cml Model

AbstractThe spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied, by using Lotka-Volterra equations. A correlated dichotomous noise acts on the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of the three species. After analyzing the time behaviour of the three species in a single site, we consider a two-dimensional spatial domain, applying a mean field approach and obtaining the time behaviour of the first and second order moments for different multiplicative noise intensities. We find noise-induced oscillations of the three species with an anticorrelated behaviour of the two preys. Finally, we compare our results with those obtained by using a coupled map lattice (CML) model, finding a good qualitative agreement. However, some quantitative discrepancies appear, that can be explained as follows: i) different stationary values occur in the two approaches; ii) in the mean field formalism the interaction between sites is extended to the whole spatial domain, conversely in the CML model the species interaction is restricted to the nearest neighbors; iii) the dynamics of the CML model is faster since an unitary time step is considered.

scholarly journals A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin–Huxley models

2020 ◽  
Vol 123 (3) ◽  
pp. 1042-1051 ◽  
Author(s):  
M. Carlu ◽  
O. Chehab ◽  
L. Dalla Porta ◽  
D. Depannemaecker ◽  
C. Héricé ◽  
...  
Keyword(s):  
Temporal Dynamics ◽  
Mean Field ◽  
Population Models ◽  
Mathematical Tool ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
Mean Field Models ◽  
Electrophysiological Recordings ◽  
The Brain ◽  
Powerful Mathematical Tool

Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin–Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

scholarly journals Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons

2017 ◽  
Author(s):  
Yann Zerlaut∗ ◽  
Sandrine Chemla ◽  
Frederic Chavane ◽  
Alain Destexhe∗
Keyword(s):  
Time Course ◽  
Field Model ◽  
Mean Field ◽  
Temporal Patterns ◽  
Analytical Description ◽  
External Input ◽  
Inhibitory Neurons ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
Spatio Temporal

AbstractVoltage-sensitive dye imaging (VSDi) has revealed fundamental properties of neocortical processing at macroscopic scales. Since for each pixel VSDi signals report the average membrane potential over hundreds of neurons, it seems natural to use a mean-field formalism to model such signals. Here, we present a mean-field model of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based synaptic interactions. We study here a network of regular-spiking (RS) excitatory neurons and fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism, together with a semi-analytic approach to the transfer function of AdEx neurons to describe the average dynamics of the coupled populations. We compare the predictions of this mean-field model to simulated networks of RS-FS cells, first at the level of the spontaneous activity of the network, which is well predicted by the analytical description. Second, we investigate the response of the network to time-varying external input, and show that the mean-field model predicts the response time course of the population. Finally, to model VSDi signals, we consider a one-dimensional ring model made of interconnected RS-FS mean-field units. We found that this model can reproduce the spatio-temporal patterns seen in VSDi of awake monkey visual cortex as a response to local and transient visual stimuli. Conversely, we show that the model allows one to infer physiological parameters from the experimentally-recorded spatio-temporal patterns.

scholarly journals Inhomogeneous mean-field approach to collective excitations near the superfluid-Mott glass transition

2021 ◽  
pp. 168526
Author(s):  
Martin Puschmann ◽  
João C. Getelina ◽  
José A. Hoyos ◽  
Thomas Vojta
Keyword(s):  
Glass Transition ◽  
Mean Field ◽  
Collective Excitations ◽  
Field Approach

scholarly journals Effect of Bjerrum pairs on electrostatic properties in an electrolyte solution near charged surfaces: A mean-field approach

2021 ◽  
Author(s):  
Jun-Sik Sin
Keyword(s):  
Electrolyte Solution ◽  
Size Effects ◽  
Mean Field ◽  
Finite Size ◽  
Ion Association ◽  
Finite Size Effects ◽  
Field Approach ◽  
Electrostatic Properties ◽  
Charged Surfaces ◽  
Orientational Ordering

In this paper, we investigate the consequences of ion association, coupled with the considerations of finite size effects and orientational ordering of Bjerrum pairs as well as ions and water...

scholarly journals Electron liquid state in the symmetric Anderson lattice

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Igor N. Karnaukhov
Keyword(s):  
Low Temperatures ◽  
Arbitrary Dimension ◽  
Mean Field ◽  
Coulomb Repulsion ◽  
Anomalous Behavior ◽  
Effective Field ◽  
Kondo Lattice ◽  
Field Approach ◽  
Cubic Lattices ◽  
Half Filling

AbstractUsing mean field approach, we provide analytical and numerical solution of the symmetric Anderson lattice for arbitrary dimension at half filling. The symmetric Anderson lattice is equivalent to the Kondo lattice, which makes it possible to study the behavior of an electron liquid in the Kondo lattice. We have shown that, due to hybridization (through an effective field due to localized electrons) of electrons with different spins and momenta $$\mathbf{k} $$ k and $$\mathbf{k} +\overrightarrow{\pi }$$ k + π → , the gap in the electron spectrum opens at half filling. Such hybridization breaks the conservation of the total magnetic momentum of electrons, the spontaneous symmetry is broken. The state of electron liquid is characterized by a large Fermi surface. A gap in the spectrum is calculated depending on the magnitude of the on-site Coulomb repulsion and value of s–d hybridization for the chain, as well as for square and cubic lattices. Anomalous behavior of the heat capacity at low temperatures in the gapped state, which is realized in the symmetric Anderson lattice, was also found.

scholarly journals Quantal description of nucleon exchange in a stochastic mean-field approach

2015 ◽  
Vol 91 (5) ◽  
Author(s):  
S. Ayik ◽  
O. Yilmaz ◽  
B. Yilmaz ◽  
A. S. Umar ◽  
A. Gokalp ◽  
...  
Keyword(s):  
Mean Field ◽  
Field Approach
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