Correlation transfer in stochastically driven oscillators over long and short time scales

Abstract

In the absence of synaptic coupling, two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams. Recent work has shown that the degree of correlation transfer from input currents to output spikes depends not only on intrinsic oscillator dynamics, but also depends on the length of the observation window over which the correlation is calculated. In this paper we use stochastic phase reduction and regular perturbations to derive the correlation of the total phase elapsed over long time scales, a quantity which provides a convenient proxy for the spike count correlation. Over short time scales, we derive the spike count correlation directly using straightforward probabilistic reasoning applied to the density of the phase difference. Our approximations show that output correlation scales with the autocorrelation of the phase resetting curve over long time scales. We also find a concise expression for the influence of the shape of the phase resetting curve on the initial slope of the output correlation over short time scales. These analytic results together with numerical simulations provide new intuitions for the recent counterintuitive finding that type I oscillators transfer correlations more faithfully than do type II over long time scales, while the reverse holds true for the better understood case of short time scales.

9 pages, 7 figures, submitted to Physical Review E

References in corpus (6)

• Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
• Stochastic phase reduction for a general class of noisy limit cycle oscillators
• Phase reduction of stochastic limit cycle oscillators
• The type II phase resetting curve is optimal for stochastic synchrony
• Double coherence resonance in neuron models driven by discrete correlated noise
• Timescales of spike-train correlation for neural oscillators with common drive

Cited by in corpus (6)

• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Qualitative changes in spike-based neural coding and synchronization at the saddle-node loop bifurcation
• Solving the 2-Dimensional Fokker-Planck Equation for Strongly Correlated Neurons
• Independent Noise Synchronizing Networks of Oscillator Networks
• Joint Statistics of Strongly Correlated Neurons via Dimensional Reduction
• The A-current and Type I / Type II transition determine collective spiking from common input