scholarly journals Coherent oscillations in balanced neural networks driven by endogenous fluctuations

2021 ◽  
Author(s):  
Matteo Di Volo ◽  
Marco Segneri ◽  
Denis Goldobin ◽  
Antonio Politi ◽  
Alessandro Torcini
Keyword(s):  
Mean Field ◽  
Planck Equation ◽  
Structural Heterogeneity ◽  
Mean Field Model ◽  
Self Consistent ◽  
Consistent Solution ◽  
The Mean ◽  
Collective Oscillations ◽  
Low Dimensional ◽  
Parameter Values

We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on the parameter values, either an asynchronous regime or periodic oscillations spontaneously emerge. Numerical simulations are compared with a mean field model based on a self-consistent Fokker-Planck equation (FPE). The FPE reproduces quite well the asynchronous dynamics in the homogeneous case by either assuming a Poissonian or renewal distribution for the incoming spike trains. An exact self consistent solution for the mean firing rate obtained in the limit of infinite in-degree allows identifying balanced regimes that can be either mean- or fluctuation-driven. A low-dimensional reduction of the FPE in terms of circular cumulants is also considered. Two cumulants suffice to reproduce the transition scenario observed in the network. The emergence of periodic collective oscillations is well captured both in the homogeneous and heterogeneous setups by the mean field models upon tuning either the connectivity, or the input DC current. In the heterogeneous situation we analyze also the role of structural heterogeneity.

CHAOTIC MEAN FIELD DYNAMICS OF A BOOLEAN NETWORK WITH RANDOM CONNECTIVITY

2007 ◽  
Vol 18 (09) ◽  
pp. 1459-1473 ◽  
Author(s):  
MALIACKAL POULO JOY ◽  
DONALD E. INGBER ◽  
SUI HUANG
Keyword(s):  
Regulatory Networks ◽  
Boolean Network ◽  
Mean Field ◽  
Period Doubling ◽  
Structural Heterogeneity ◽  
Boolean Networks ◽  
Analytical Treatment ◽  
Random Boolean Networks ◽  
The Mean ◽  
Parameter Values

Random Boolean networks have been used as simple models of gene regulatory networks, enabling the study of the dynamic behavior of complex biological systems. However, analytical treatment has been difficult because of the structural heterogeneity and the vast state space of these networks. Here we used mean field approximations to analyze the dynamics of a class of Boolean networks in which nodes have random degree (connectivity) distributions, characterized by the mean degree k and variance D. To achieve this we generalized the simple cellular automata rule 126 and used it as the Boolean function for all nodes. The equation for the evolution of the density of the network state is presented as a one-dimensional map for various input degree distributions, with k and D as the control parameters. The mean field dynamics is compared with the data obtained from the simulations of the Boolean network. Bifurcation diagrams and Lyapunov exponents for different parameter values were computed for the map, showing period doubling route to chaos with increasing k. Onset of chaos was delayed (occurred at higher k) with the increase in variance D of the connectivity. Thus, the network tends to be less chaotic when the heterogeneity, as measured by the variance of connectivity, was higher.

A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

2009 ◽  
Vol 623 ◽  
pp. 283-316 ◽  
Author(s):  
DIRK M. LUCHTENBURG ◽  
BERT GÜNTHER ◽  
BERND R. NOACK ◽  
RUDIBERT KING ◽  
GILEAD TADMOR
Keyword(s):  
High Frequency ◽  
Field Model ◽  
Mean Field ◽  
Low Frequency ◽  
Navier Stokes ◽  
Mean Field Model ◽  
High Lift ◽  
The Mean ◽  
Generalized Mean ◽  
Low Dimensional

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier–Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

scholarly journals Calculation of the T-P phase diagrams for the halogenomethane compounds (CCl-=SUB=-4-n-=/SUB=-Br-=SUB=-n-=/SUB=-, n=0, 1, 2, 4) using the mean field theory -=SUP=-*-=/SUP=-

2019 ◽  
Vol 61 (2) ◽  
pp. 339
Author(s):  
H. Yurtseven ◽  
S.B. Isik ◽  
E. Kilit Dogan
Keyword(s):  
Phase Diagrams ◽  
Mean Field Theory ◽  
Mean Field ◽  
Face Centered Cubic ◽  
Mean Field Model ◽  
Phase Line ◽  
Component Systems ◽  
Two Component Systems ◽  
The Mean ◽  
Face Centered

AbstractThe T – P phase diagrams of the halogenomethane compounds (CCl_4 – _ n Br_ n , n = 0, 1, 2, 4) are calculated using a mean field model. By expanding the free energy in terms of the order parameters for the transitions of the liquid (L), rhombohedral (R), face-centered cubic (FCC) and monoclinic (M) phases in those compounds, the phase line equations are derived and they are fitted to the experimental data from the literature. This method of calculating the T – P phase diagram is satisfactory to explain the T – P measurements for the halogenomethane compounds and it can also be applied to two-component systems.

CURRENTS, SPIN DENSITIES AND MEAN-FIELD FORM FACTORS IN ROTATING NUCLEI: A SEMI-CLASSICAL APPROACH

2004 ◽  
Vol 13 (01) ◽  
pp. 225-233 ◽  
Author(s):  
J. BARTEL ◽  
K. BENCHEIKH ◽  
P. QUENTIN
Keyword(s):  
Mean Field ◽  
Form Factors ◽  
Spin Vector ◽  
Self Consistent ◽  
Field Form ◽  
Local Densities ◽  
The Mean ◽  
Self Consistency ◽  
Spin Densities ◽  
Rotating Nuclei

We present self-consistent semi-classical local densities characterising the structure of rotating nuclei. A particular emphasis is put on those densities which are generated by the breaking of time-reversal symmetry through the cranking piece of the Routhian, namely the current density and the spin vector density. Our approach which is based on the Extended-Thomas-Fermi method goes beyond the Inglis cranking approach and contains naturally the Thouless-Valatin self-consistency terms expressing the response of the mean field to the time-odd part of the density matrix.

Single-Crystal Magnetic Properties of [Co(NH3)5(OH2)] [Cr(CN)6] Between 2 and 300 K

1992 ◽  
Vol 45 (11) ◽  
pp. 1899 ◽  
Author(s):  
PA Reynolds ◽  
CD Delfs ◽  
BN Figgis ◽  
B Moubaraki ◽  
KS Murray
Keyword(s):  
Ising Model ◽  
Field Model ◽  
Mean Field ◽  
Zero Field ◽  
Spin Orbit Coupling ◽  
Zero Field Splitting ◽  
Magnetic Exchange Interaction ◽  
Mean Field Model ◽  
Magnetic Exchange ◽  
The Mean

The magnetic susceptibilities along and perpendicular to the c axis (hexagonal setting) between 2.0 and 300 K at a magnetic field of 1.00 T, and the magnetizations at field strengths up to 5.00 T, are presented for single crystals of [Co(NH3)5(OH2)] [Cr(CN)6]. The results are interpreted in terms of zero-field splitting (2D) of the ground 4A2g term by spin-orbit coupling and of magnetic exchange interaction between the chromium atoms. The magnetic exchange is modelled as one of Ising or mean-field in type. The exchange is found to be quite small: J = -0.18(6) cm-1 if the Ising model is employed, and -0.03(1) cm-1 for the mean-field model. The model adopted for the exchange has a strong influence on the value of the parameter D obtained. When the Ising model is used D is deduced to be -0.28(9) cm-l; when the mean-field model is used D is -0.14(4) cm-l. The g-values deduced are in agreement with those from e.s.r. measurements at higher temperatures and do not depend on the exchange model. In any case, D is found to be sufficiently large that it must be considered in a polarized neutron diffraction experiment on the compound.

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