scholarly journals Dynamical Bridge Between Song Degradation and Neural Plasticity

2021 ◽  
Author(s):  
Jie Zang ◽  
Shenquan Liu
Keyword(s):  
Neural Plasticity ◽  
Field Model ◽  
Mean Field ◽  
Stable Limit Cycle ◽  
Bistable System ◽  
Stable Node ◽  
Stable Limit ◽  
Mean Field Model ◽  
Mean Field Equations ◽  
The Mean

Abstract High dimensionality and complexity are the main difficulties of the study over network dynamics. Recently, Wilten Nicola proposed the mean field theory to research the bifurcations that the full networks display. Here, we use his approach on the birdsong neural network. Our previous work has shown that AFP could adjust the synapse conductance of nucleus RA and change RA’s firing patterns, eventually leading to song degradation. To understand the dynamical principle behind this, we use a technique to reduce the RA network to a mean field model, in the form of a system of switching ordinary differential equations. Numerical results have shown that the mean field equations can qualitatively and quantitatively describe the behavior of nucleus RA. Based on the non-smooth bifurcation analysis of the mean field model, we determine that there is a subcritical-Andronov-Hopf bifurcation at a particular stimulation, which can explain the role of AFP during song degradation. The results indicate that we can see AFP’s adjustment in RA synapse conductance as the adjustment of initial value in the bistable system. More precisely, during song degradation, the mean field system would transform to a stable node (corresponding to distorted songs) rather than a stable limit cycle (corresponding to normal songs).

scholarly journals Dynamics of a Large-Scale Spiking Neural Network with Quadratic Integrate-and-Fire Neurons

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Weijie Ye
Keyword(s):  
Neural Network ◽  
Large Scale ◽  
Field Model ◽  
Network Dynamics ◽  
Mean Field ◽  
Spiking Neural Network ◽  
Stable Limit ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
The Mean

Since the high dimension and complexity of the large-scale spiking neural network, it is difficult to research the network dynamics. In recent decades, the mean-field approximation has been a useful method to reduce the dimension of the network. In this study, we construct a large-scale spiking neural network with quadratic integrate-and-fire neurons and reduce it to a mean-field model to research the network dynamics. We find that the activity of the mean-field model is consistent with the network activity. Based on this agreement, a two-parameter bifurcation analysis is performed on the mean-field model to understand the network dynamics. The bifurcation scenario indicates that the network model has the quiescence state, the steady state with a relatively high firing rate, and the synchronization state which correspond to the stable node, stable focus, and stable limit cycle of the system, respectively. There exist several stable limit cycles with different periods, so we can observe the synchronization states with different periods. Additionally, the model shows bistability in some regions of the bifurcation diagram which suggests that two different activities coexist in the network. The mechanisms that how these states switch are also indicated by the bifurcation curves.

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.

scholarly journals Phase diagram of the mean field model of simplicial gravity

1999 ◽  
Vol 542 (1-2) ◽  
pp. 413-424 ◽  
Author(s):  
P. Bialas ◽  
Z. Burda ◽  
D. Johnston
Keyword(s):  
Phase Diagram ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
The Mean

A Phase Diagram for the Ice VI–VII–VIII Transitions

1998 ◽  
Vol 12 (08) ◽  
pp. 271-279 ◽  
Author(s):  
H. Yurtseven ◽  
S. Salihoğlu
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Field Model ◽  
Mean Field ◽  
Calculated Phase Diagram ◽  
Mean Field Model ◽  
Phase Line ◽  
Calculated Phase ◽  
The Mean ◽  
T Phase

In this study we obtain the P–T phase diagram for the ice VI–VII–VIII phase transitions by means of the mean field model developed here. We have fitted the experimentally measured P–T data to our phase line equations. Our calculated phase diagram describes adequately the observed behavior of the ice VI–VII–VIII phase transitions.

COMPETITION AND PREDATION IN A THREE SPECIES MODEL

2006 ◽  
Vol 17 (11) ◽  
pp. 1629-1645 ◽  
Author(s):  
JANUSZ SZWABIǸSKI ◽  
ANDRZEJ PȨKALSKI ◽  
KAMIL TROJAN
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
Agent Based ◽  
Interacting Species ◽  
Stochastic Fluctuations ◽  
The Mean ◽  
Large Systems ◽  
Access To Food ◽  
Type Of Behavior

A model of dynamics of three interacting species is presented. Two of the species are prey and one is predator, which feeds on both prey, however with some preference to one type. Prey compete for space (breeding) although they always have access to food. Predators in order to survive and reproduce must catch prey, otherwise they die of hunger. The dynamics of the model is found via differential equations in the mean-field like approach and through computer simulations for agent-based method. We show that the coexistence of the three species is possible in the mean-field model, provided the preference of the predators is small, whereas from simulation it follows that the stochastic fluctuations drive, generally, one of the prey populations into extinction. We have found a different type of behavior for small and large systems and a rather unexpected dependence of the coexistence chance of the preference parameter in bigger lattices.

scholarly journals Mean field approximation of network of biophysical neurons driven by conductance-based ion exchange dynamics

2021 ◽  
Author(s):  
Abhirup Bandyopadhyay ◽  
Spase Petkoski ◽  
Viktor Jirsa
Keyword(s):  
Ion Exchange ◽  
Molecular Mechanisms ◽  
Field Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Mean Field Model ◽  
Ion Concentrations ◽  
The Mean ◽  
Locally Homogeneous

Changes in extracellular ion concentrations are known to modulate neuronal excitability and play a major role in controlling the neuronal firing rate, not just during the healthy homeostasis, but also in pathological conditions such as epilepsy. The microscopic molecular mechanisms of field effects are understood, but the precise correspondence between the microscopic mechanisms of ion exchange in the cellular space of neurons and the macroscopic behavior of neuronal populations remains to be established. We derive a mean field model of a population of Hodgkin Huxley type neurons. This model links the neuronal intra- and extra-cellular ion concentrations to the mean membrane potential and the mean synaptic input in terms of the synaptic conductance of the locally homogeneous mesoscopic network and can describe various brain activities including multi-stability at resting states, as well as more pathological spiking and bursting behaviors, and depolarizations. The results from the analytical solution of the mean field model agree with the mean behavior of numerical simulations of large-scale networks of neurons. The mean field model is analytically exact for non-autonomous ion concentration variables and provides a mean field approximation in the thermodynamic limit, for locally homogeneous mesoscopic networks of biophysical neurons driven by an ion exchange mechanism. These results may provide the missing link between high-level neural mass approaches which are used in the brain network modeling and physiological parameters that drive the neuronal dynamics.

Calculation of the thermodynamic quantities of perovskite metal organics DMAKCr and perovskite HyFe close to the weakly first-order relaxor-like structural transformation using the mean field theory

2019 ◽  
Vol 33 (11) ◽  
pp. 1950103 ◽  
Author(s):  
H. Yurtseven ◽  
Ö. Tarı
Keyword(s):  
Field Theory ◽  
Field Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Excess Heat Capacity ◽  
Mean Field Model ◽  
First Order ◽  
Entropy Formula ◽  
Inverse Susceptibility ◽  
The Mean

Weakly first-order or nearly second-order phase transitions occurring in metal–organic frameworks (MOFs), particularly in DMAKCr and perovskite HyFe, are studied under the mean field model by using the observed data from the literature. In this work, mainly thermal and magnetic properties among various physical properties which have been reported in the literature for those MOFs are studied by the mean field theory. By expanding the free energy in terms of the magnetization (order parameter), the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S), latent heat (L), magnetization (M) and the inverse susceptibility ([Formula: see text]) are calculated as a function of temperature close to the weakly first-order phase transition within the Landau phenomenological model which is fitted to the experimental data from the literature for C[Formula: see text] (DMAKCr and perovskite HyFe) and for magnetization M (HyFe). Our predictions of the excess heat capacity ([Formula: see text]C[Formula: see text]) and entropy ([Formula: see text]S) agree below T[Formula: see text] with the observed data within the temperature intervals studied for DMAKCr and perovskite HyFe. From our predictions, we find that magnetization decreases continuously whereas the inverse susceptibility decreases linearly with increasing temperature toward the transition temperature in those MOFs as expected for a weakly first-order transition from the mean field model.

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