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Stabilizing synchrony by inhomogeneity.

Bolhasani E, Valizadeh A - Sci Rep (2015)

Bottom Line: We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips.Small inhomogeneity-mismatch in the intrinsic firing rate of the neurons-can stabilize the phase locking and lead to more precise relative spike timing of the two neurons.The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.

View Article: PubMed Central - PubMed

Affiliation: Institute for Advanced Studies in Basic Sciences, Department of physics, Zanjan, 45137-66731, Iran.

ABSTRACT
We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity-mismatch in the intrinsic firing rate of the neurons-can stabilize the phase locking and lead to more precise relative spike timing of the two neurons. The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.

No MeSH data available.


Related in: MedlinePlus

The cross-correlogram of spike trains of two neurons C(τ) shows that in presence of the firing rate mismatch cross correlation is increased.The left panel shows the results for LIF neurons and the level of maximum correlation is shown in the inset to highlight the increase due to the inhomogeneity. In the right panel the results are presented for two Wang-Buzsaki (WB) neurons. The parameters for both simulations are given in the supplemantary material.
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f3: The cross-correlogram of spike trains of two neurons C(τ) shows that in presence of the firing rate mismatch cross correlation is increased.The left panel shows the results for LIF neurons and the level of maximum correlation is shown in the inset to highlight the increase due to the inhomogeneity. In the right panel the results are presented for two Wang-Buzsaki (WB) neurons. The parameters for both simulations are given in the supplemantary material.

Mentions: The above equation is the same as Eq. (7) by substituting ρ(ϕ*) with . Figure 2B shows maximum value of cross-correlation versus frequency mismatch for two canonical type-I phase oscillators for different values of noise to coupling ratio which is resulted from direct integration of Eq. (7). The result shows that the maximum cross-correlation of the spike trains of the oscillators would be also maximum when the neurons are not identical. This is a consequence of more precise relative spike timing of the two neurons in presence of inhomogeneity. In Fig. 3 we have shown the cross-correlogram for LIF oscillators and also for the WB model neurons. While for both the models small inhomogeneity increases correlation of the spike trains, for the WB model neurons inhomogeneity also moves the maximum correlation to the non-zero phase lags similar to the canonical type-I phase oscillators.


Stabilizing synchrony by inhomogeneity.

Bolhasani E, Valizadeh A - Sci Rep (2015)

The cross-correlogram of spike trains of two neurons C(τ) shows that in presence of the firing rate mismatch cross correlation is increased.The left panel shows the results for LIF neurons and the level of maximum correlation is shown in the inset to highlight the increase due to the inhomogeneity. In the right panel the results are presented for two Wang-Buzsaki (WB) neurons. The parameters for both simulations are given in the supplemantary material.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4559804&req=5

f3: The cross-correlogram of spike trains of two neurons C(τ) shows that in presence of the firing rate mismatch cross correlation is increased.The left panel shows the results for LIF neurons and the level of maximum correlation is shown in the inset to highlight the increase due to the inhomogeneity. In the right panel the results are presented for two Wang-Buzsaki (WB) neurons. The parameters for both simulations are given in the supplemantary material.
Mentions: The above equation is the same as Eq. (7) by substituting ρ(ϕ*) with . Figure 2B shows maximum value of cross-correlation versus frequency mismatch for two canonical type-I phase oscillators for different values of noise to coupling ratio which is resulted from direct integration of Eq. (7). The result shows that the maximum cross-correlation of the spike trains of the oscillators would be also maximum when the neurons are not identical. This is a consequence of more precise relative spike timing of the two neurons in presence of inhomogeneity. In Fig. 3 we have shown the cross-correlogram for LIF oscillators and also for the WB model neurons. While for both the models small inhomogeneity increases correlation of the spike trains, for the WB model neurons inhomogeneity also moves the maximum correlation to the non-zero phase lags similar to the canonical type-I phase oscillators.

Bottom Line: We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips.Small inhomogeneity-mismatch in the intrinsic firing rate of the neurons-can stabilize the phase locking and lead to more precise relative spike timing of the two neurons.The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.

View Article: PubMed Central - PubMed

Affiliation: Institute for Advanced Studies in Basic Sciences, Department of physics, Zanjan, 45137-66731, Iran.

ABSTRACT
We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity-mismatch in the intrinsic firing rate of the neurons-can stabilize the phase locking and lead to more precise relative spike timing of the two neurons. The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.

No MeSH data available.


Related in: MedlinePlus