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Dynamic Control of Synchronous Activity in Networks of Spiking Neurons

View Article: PubMed Central - PubMed

ABSTRACT

Oscillatory brain activity is believed to play a central role in neural coding. Accumulating evidence shows that features of these oscillations are highly dynamic: power, frequency and phase fluctuate alongside changes in behavior and task demands. The role and mechanism supporting this variability is however poorly understood. We here analyze a network of recurrently connected spiking neurons with time delay displaying stable synchronous dynamics. Using mean-field and stability analyses, we investigate the influence of dynamic inputs on the frequency of firing rate oscillations. We show that afferent noise, mimicking inputs to the neurons, causes smoothing of the system’s response function, displacing equilibria and altering the stability of oscillatory states. Our analysis further shows that these noise-induced changes cause a shift of the peak frequency of synchronous oscillations that scales with input intensity, leading the network towards critical states. We lastly discuss the extension of these principles to periodic stimulation, in which externally applied driving signals can trigger analogous phenomena. Our results reveal one possible mechanism involved in shaping oscillatory activity in the brain and associated control principles.

No MeSH data available.


As period driving amplitude increases, global oscillations accelerate and become gradually more linear.The network mean activity  is shown (top panels) with a close up view of a few cycles (center panels) with the associated response function (bottom panels), for various input amplitudes. A. Io = 0.01. B. Io = 0.1. C. Io = 1.0. Other parameters are α = 100Hz, β = 2500/mV, g = −2mV/Hz, s = 4mV/Hz, τ = 25ms.
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pone.0161488.g005: As period driving amplitude increases, global oscillations accelerate and become gradually more linear.The network mean activity is shown (top panels) with a close up view of a few cycles (center panels) with the associated response function (bottom panels), for various input amplitudes. A. Io = 0.01. B. Io = 0.1. C. Io = 1.0. Other parameters are α = 100Hz, β = 2500/mV, g = −2mV/Hz, s = 4mV/Hz, τ = 25ms.

Mentions: Taking a closer look at the slope of the new response function , we finddF′˜dμ<0(31)for , and otherwise. Hence the nonlinear response function flattens and becomes increasingly linear for increasing μ similar to the stochastic case for increased noise level. Fig 5 (bottom panels) shows for three different stimulus amplitudes, i.e. different values of , confirming this analytical finding.


Dynamic Control of Synchronous Activity in Networks of Spiking Neurons
As period driving amplitude increases, global oscillations accelerate and become gradually more linear.The network mean activity  is shown (top panels) with a close up view of a few cycles (center panels) with the associated response function (bottom panels), for various input amplitudes. A. Io = 0.01. B. Io = 0.1. C. Io = 1.0. Other parameters are α = 100Hz, β = 2500/mV, g = −2mV/Hz, s = 4mV/Hz, τ = 25ms.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC5036852&req=5

pone.0161488.g005: As period driving amplitude increases, global oscillations accelerate and become gradually more linear.The network mean activity is shown (top panels) with a close up view of a few cycles (center panels) with the associated response function (bottom panels), for various input amplitudes. A. Io = 0.01. B. Io = 0.1. C. Io = 1.0. Other parameters are α = 100Hz, β = 2500/mV, g = −2mV/Hz, s = 4mV/Hz, τ = 25ms.
Mentions: Taking a closer look at the slope of the new response function , we finddF′˜dμ<0(31)for , and otherwise. Hence the nonlinear response function flattens and becomes increasingly linear for increasing μ similar to the stochastic case for increased noise level. Fig 5 (bottom panels) shows for three different stimulus amplitudes, i.e. different values of , confirming this analytical finding.

View Article: PubMed Central - PubMed

ABSTRACT

Oscillatory brain activity is believed to play a central role in neural coding. Accumulating evidence shows that features of these oscillations are highly dynamic: power, frequency and phase fluctuate alongside changes in behavior and task demands. The role and mechanism supporting this variability is however poorly understood. We here analyze a network of recurrently connected spiking neurons with time delay displaying stable synchronous dynamics. Using mean-field and stability analyses, we investigate the influence of dynamic inputs on the frequency of firing rate oscillations. We show that afferent noise, mimicking inputs to the neurons, causes smoothing of the system&rsquo;s response function, displacing equilibria and altering the stability of oscillatory states. Our analysis further shows that these noise-induced changes cause a shift of the peak frequency of synchronous oscillations that scales with input intensity, leading the network towards critical states. We lastly discuss the extension of these principles to periodic stimulation, in which externally applied driving signals can trigger analogous phenomena. Our results reveal one possible mechanism involved in shaping oscillatory activity in the brain and associated control principles.

No MeSH data available.