Synchronization of pulse-coupled biological oscillators
SIAM Journal on Applied Mathematics
Dynamics of functional coupling in the cerebral cortex: an attempt at a model-based interpretation
Proceedings of the NATO advanced research workshop and EGS topical workshop on Chaotic advection, tracer dynamics and turbulent dispersion
Synchrony in excitatory neural networks
Neural Computation
Dynamical cell assembly hypothesis—theoretical possibility of spatio-temporal coding in the cortex
Neural Networks - 1996 Special issue: four major hypotheses in neuroscience
Mathematical physiology
Chaotic balanced state in a model of cortical circuits
Neural Computation
Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
Spatiotemporal spike-encoding of a continuous external signal
Neural Computation
Dynamics of Strongly Coupled Spiking Neurons
Neural Computation
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Neuronal information processing is often studied on the basis of spiking patterns. The relevant statistics such as firing rates calculated with the peri-stimulus time histogram are obtained by averaging spiking patterns over many experimental runs. However, animals should respond to one experimental stimulation in real situations, and what is available to the brain is not the trial statistics but the population statistics. Consequently, physiological ergodicity, namely, the consistency between trial averaging and population averaging, is implicitly assumed in the data analyses, although it does not trivially hold true. In this letter, we investigate how characteristics of noisy neural network models, such as single neuron properties, external stimuli, and synaptic inputs, affect the statistics of firing patterns. In particular, we show that how high membrane potential sensitivity to input fluctuations, inability of neurons to remember past inputs, external stimuli with large variability and temporally separated peaks, and relatively few contributions of synaptic inputs result in spike trains that are reproducible over many trials. The reproducibility of spike trains and synchronous firing are contrasted and related to the ergodicity issue. Several numerical calculations with neural network examples are carried out to support the theoretical results.