Stability Analysis on Sparsely Encoded Associative Memory with Short-Term Synaptic Dynamics

2017 ◽  
Vol 27 (10) ◽  
pp. 1730034
Author(s):  
Muyuan Xu ◽  
Yuichi Katori ◽  
Kazuyuki Aihara
Keyword(s):  
Stability Analysis ◽  
Associative Memory ◽  
Memory Retrieval ◽  
Field Model ◽  
Mean Field ◽  
Detailed Structure ◽  
Short Term ◽  
Mean Field Model ◽  
Synaptic Dynamics ◽  
The Stability

This study investigates the stability of sparsely encoded associative memory in a network composed of stochastic neurons. The incorporation of short-term synaptic dynamics significantly changes the stability with respect to synaptic properties. Various states including static and oscillatory states are found in the network dynamics. Specifically, the sparseness of memory patterns raises the problem of spurious states. A mean field model is used to analyze the detailed structure in the stability and show that the performance of memory retrieval is recovered by appropriate feedback.

scholarly journals Size distribution and structure of Barchan dune fields

2011 ◽  
Vol 18 (4) ◽  
pp. 455-467 ◽  
Author(s):  
O. Durán ◽  
V. Schwämmle ◽  
P. G. Lind ◽  
H. J. Herrmann
Keyword(s):  
Size Distribution ◽  
Field Model ◽  
Cooperative Behavior ◽  
Mean Field ◽  
Mean Field Model ◽  
Dune Field ◽  
Barchan Dune ◽  
The Stability ◽  
Mobile Dunes ◽  
Selection Of

Abstract. Barchans are isolated mobile dunes often organized in large dune fields. Dune fields seem to present a characteristic dune size and spacing, which suggests a cooperative behavior based on dune interaction. In Duran et al. (2009), we propose that the redistribution of sand by collisions between dunes is a key element for the stability and size selection of barchan dune fields. This approach was based on a mean-field model ignoring the spatial distribution of dune fields. Here, we present a simplified dune field model that includes the spatial evolution of individual dunes as well as their interaction through sand exchange and binary collisions. As a result, the dune field evolves towards a steady state that depends on the boundary conditions. Comparing our results with measurements of Moroccan dune fields, we find that the simulated fields have the same dune size distribution as in real fields but fail to reproduce their homogeneity along the wind direction.

The theory of competing nematic phases of comb polymers

1988 ◽  
Vol 417 (1852) ◽  
pp. 213-233 ◽  
Keyword(s):  
Field Model ◽  
Main Chain ◽  
Mean Field ◽  
Universal Functions ◽  
Mean Field Model ◽  
Chain Flexibility ◽  
Comb Polymers ◽  
Qualitative And Quantitative ◽  
Nematic Phases ◽  
The Stability

Comb polymers have been proposed to exhibit a variety of nematic states according to the relative nematic tendencies of the backbone and teeth, and the molecular attachment of the two. The equilibria of such nematic phases with each other and with the isotropic state can be described by a mean field model, which combines a Maier‒Saupe theory of con­ventional liquid crystals and the worm concept of semiflexible polymers. Here the model is solved analytically in terms of universal functions. Graphical constructions on the free energy reminiscent of the Maxwell area rules are derived. The method allows both qualitative and quantitative conclusions to be made of the shape and gradients of phase diagrams. Triple points and a critical point inside one of the nematic phases are predicted. The stability of equilibria is examined. The occurrence of re-entrant nematic phases is identified as a consequence of the main-chain flexibility.

scholarly journals A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation

2020 ◽  
Vol 32 (9) ◽  
pp. 1615-1634 ◽  
Author(s):  
Richard Gast ◽  
Helmut Schmidt ◽  
Thomas R. Knösche
Keyword(s):  
Population Dynamics ◽  
Phase Transitions ◽  
Steady State ◽  
Field Model ◽  
Mean Field ◽  
Short Term ◽  
Mean Field Model ◽  
Neural Communication ◽  
Short Term Adaptation ◽  
The Mean

Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between bursting and non-bursting states, mean-field descriptions of macroscopic bursting behavior are a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons and examine whether states of collective bursting behavior can arise from short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. Analyzing the mean-field model via bifurcation analysis, we find that bursting behavior emerges for both types of short-term adaptation. This bursting behavior can coexist with steady-state behavior, providing a bistable regime that allows for transient switches between synchronized and nonsynchronized states of population dynamics. For all of these findings, we demonstrate a close correspondence between the spiking neural network and the mean-field model. Although the mean-field model has been derived under the assumptions of an infinite population size and all-to-all coupling inside the population, we show that this correspondence holds even for small, sparsely coupled networks. In summary, we provide mechanistic descriptions of phase transitions between bursting and steady-state population dynamics, which play important roles in both healthy neural communication and neurological disorders.

scholarly journals Ill-posedness of the mean-field model of superconducting vortices and a possible regularisation

2000 ◽  
Vol 11 (2) ◽  
pp. 137-152 ◽  
Author(s):  
G. RICHARDSON ◽  
B. STOTH
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Field Model ◽  
Mean Field ◽  
Average Density ◽  
Mean Field Model ◽  
Superconducting Vortices ◽  
Vorticity Vector ◽  
Ill Posed ◽  
The Mean

We conjecture that the mean-field model of superconducting vortices given in [10] is ill-posed wherever the electric current j has some component in the same direction as the vorticity vector ω (which gives the average density and direction of the superconducting vortices). The conjecture is illustrated with a linear stability analysis of a certain solution to the model. A regularised model is then proposed, and this is used to demonstrate the instability of force-free steady states in a certain geometry.

DYNAMICS OF A LARGE ARRAY OF GLOBALLY COUPLED LASERS WITH DISTRIBUTED FREQUENCIES

2001 ◽  
Vol 11 (09) ◽  
pp. 2359-2374 ◽  
Author(s):  
RICARDO A. OLIVA ◽  
STEVEN H. STROGATZ
Keyword(s):  
Field Model ◽  
Natural Frequencies ◽  
Phase Locking ◽  
Mean Field ◽  
Large Array ◽  
Solid State Lasers ◽  
Mean Field Model ◽  
Coupled Nonlinear Oscillators ◽  
Coupled Lasers ◽  
The Stability

We analyze a mean-field model for a large array of coupled solid-state lasers with randomly distributed natural frequencies. Using techniques developed previously for coupled nonlinear oscillators, we derive exact formulas for the stability boundaries of the phase locked, incoherent, and off states, as functions of the coupling and pump strength and the spread of natural frequencies. For parameters in the intermediate regime between total incoherence and perfect phase locking, numerical simulations reveal a variety of unsteady collective states in which all the lasers' intensities vary periodically, quasiperiodically, or chaotically.

scholarly journals Quark mean-field model for single and double   and   hypernuclei

2014 ◽  
Vol 2014 (1) ◽  
pp. 13D02-0 ◽  
Author(s):  
J. N. Hu ◽  
A. Li ◽  
H. Shen ◽  
H. Toki
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Mean Field Model

EVOLUTION OF SHELL STRUCTURE IN NUCLEI

2011 ◽  
Vol 20 (08) ◽  
pp. 1663-1675 ◽  
Author(s):  
A. BHAGWAT ◽  
Y. K. GAMBHIR
Keyword(s):  
Shell Structure ◽  
Crucial Role ◽  
Field Model ◽  
Mean Field ◽  
Mass Region ◽  
The Other ◽  
Mean Field Model ◽  
Relativistic Mean Field ◽  
Shell Closures ◽  
Low Mass

Systematic investigations of the pairing and two-neutron separation energies which play a crucial role in the evolution of shell structure in nuclei, are carried out within the framework of relativistic mean-field model. The shell closures are found to be robust, as expected, up to the lead region. New shell closures appear in low mass region. In the superheavy region, on the other hand, it is found that the shell closures are not as robust, and they depend on the particular combinations of neutron and proton numbers. Effect of deformation on the shell structure is found to be marginal.

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