Analytical condition for synchrony in a neural network with two periodic inputs.

@article{Hashizume2013AnalyticalCF,
  title={Analytical condition for synchrony in a neural network with two periodic inputs.},
  author={Yoichiro Hashizume and Osamu Araki},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={87 1},
  pages={
          012713
        }
}
  • Y. Hashizume, O. Araki
  • Published 13 December 2012
  • Biology
  • Physical review. E, Statistical, nonlinear, and soft matter physics
In this study, we apply a mean-field theory to the neural network model with two periodic inputs in order to clarify the conditions of synchronies. This mean-field theory yields a self-consistent condition for the synchrony and enables us to study the effects of synaptic connections for the behavior of neural networks. Then, we obtain a condition of synaptic connections for the synchrony with the cycle time T. The neurons in neural networks receive sensory inputs and top-down inputs from… 
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References

SHOWING 1-10 OF 78 REFERENCES
Mean-field theory of a plastic network of integrate-and-fire neurons.
TLDR
A self-consistent mean-field theory is applied to the network of integrate-and-fire neurons to obtain the mean activity level for the system as a function of the mean synaptic weight, which predicts a first-order transition and hysteresis between a noise-dominated regime and a regime of persistent neural activity.
Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex.
TLDR
This work finds that if the average synaptic potentiation (LTP) is too low, no stimulus specific activity manifests itself in the delay period, and investigates self-sustaining stable states (attractors) in networks of integrate-and-fire neurons.
Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons
  • N. Brunel
  • Biology
    Journal of Computational Neuroscience
  • 2004
The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous…
STDP Provides the Substrate for Igniting Synfire Chains by Spatiotemporal Input Patterns
TLDR
Numerical experiments show that the spiking neural network generates a single global synchrony whose relative timing depends on the input spatiotemporal pattern and the neural network structure, which implies that theSpike-timing-dependent synaptic plasticity learns the transformation from spatiotmporal to temporal information.
A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input
TLDR
The focus of this review is upon the mathematical techniques that give the time distribution of output spikes, namely stochastic differential equations and the Fokker–Planck equation.
A THEORETICAL ANALYSIS OF NEURONAL VARIABILITY.
  • R. Stein
  • Psychology
    Biophysical journal
  • 1965
Synaptic noise and other sources of randomness in motoneuron interspike intervals.
TLDR
None of the models in the literature has utilized the measured properties of either the steady-state synaptic input or of the spike-generating mechanism of the very neuron whose interval variability they wished to predict.
A Stimulus-Response Neural Network Model Prepared by Top-Down Signals
TLDR
A fundamental neural network model is proposed, which can trigger the movement in response to a specific sensory input using top-down signals, and appropriate pairing of top-downs to 1st and 2nd layers enables the circuits to execute an arbitrary stimulus-response behavior.
Some models of neuronal variability.
Temporal characteristics of the predictive synchronous firing modeled by spike-timing-dependent plasticity.
TLDR
This model suggests that the important characteristics of predictive synchronous firing, which were previously attributed to an animal's higher cognitive function, can emerge from a synaptic-level mechanism.
...
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