Limits...
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

(A) The steady state phase difference distributions ρ(ϕ) for three levels of heterogeneity. Distributions have become narrower as mismatch is increased. Solid lines show the analytic result Eq. (6) and the bar graph presents the numerical results by direct integration of Eq. (2). Dashed vertical lines show the position of the fixed points of deterministic equations. (B) The maximum value of ρ(ϕ) is plotted against frequency mismatch for two different values of the ratio of noise strength to effective coupling . (C) The most probable phase difference (shown by dashed line in A) is shown for three values of α. In the presence of noise (α ≠ 0) the most probable phase difference is different from the fixed point of the deterministic equations (black curve α = 0).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4559804&req=5

f2: (A) The steady state phase difference distributions ρ(ϕ) for three levels of heterogeneity. Distributions have become narrower as mismatch is increased. Solid lines show the analytic result Eq. (6) and the bar graph presents the numerical results by direct integration of Eq. (2). Dashed vertical lines show the position of the fixed points of deterministic equations. (B) The maximum value of ρ(ϕ) is plotted against frequency mismatch for two different values of the ratio of noise strength to effective coupling . (C) The most probable phase difference (shown by dashed line in A) is shown for three values of α. In the presence of noise (α ≠ 0) the most probable phase difference is different from the fixed point of the deterministic equations (black curve α = 0).

Mentions: Figure 2A shows the steady state phase difference distribution for different values of the frequency mismatch for QIF neuronal oscillators. It can be seen that the distribution becomes narrower (with a more pronounced peak) with increasing frequency mismatch while the neurons remain in 1:1 locked state, i.e. for the mismatch in the range . This reflects a larger basin of attraction for the locked state when mismatch is increased from zero. Most robust locking occurs for when the basin of attraction is symmetric around the stable fixed point. Furthermore, the asymmetry of the basin of attraction causes the distribution of the phase differences not to peak in the fixed point of the deterministic equation, determined by . In turn, in presence of noise the location of maximum phase difference satisfies,which is derived by taking the derivative of ρ(ϕ) with respect to ϕ, equal to zero. The location of the most probable phase difference as a function of mismatch, determined by Eq. (7), is plotted in Fig. 2C for different values of the noise amplitude as well as for the noiseless system which coincides with the location of the fixed point. Presence of noise inclines the distribution to larger phase differences for small values of frequency mismatch. The maximum difference between the location of most probable phase difference between noiseless state and noisy state is seen near which reflects the most asymmetric basin of attraction for the locked state and in turn the locations coincide when ϕ* = π/2 where the basin of attraction is symmetric.


Stabilizing synchrony by inhomogeneity.

Bolhasani E, Valizadeh A - Sci Rep (2015)

(A) The steady state phase difference distributions ρ(ϕ) for three levels of heterogeneity. Distributions have become narrower as mismatch is increased. Solid lines show the analytic result Eq. (6) and the bar graph presents the numerical results by direct integration of Eq. (2). Dashed vertical lines show the position of the fixed points of deterministic equations. (B) The maximum value of ρ(ϕ) is plotted against frequency mismatch for two different values of the ratio of noise strength to effective coupling . (C) The most probable phase difference (shown by dashed line in A) is shown for three values of α. In the presence of noise (α ≠ 0) the most probable phase difference is different from the fixed point of the deterministic equations (black curve α = 0).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: (A) The steady state phase difference distributions ρ(ϕ) for three levels of heterogeneity. Distributions have become narrower as mismatch is increased. Solid lines show the analytic result Eq. (6) and the bar graph presents the numerical results by direct integration of Eq. (2). Dashed vertical lines show the position of the fixed points of deterministic equations. (B) The maximum value of ρ(ϕ) is plotted against frequency mismatch for two different values of the ratio of noise strength to effective coupling . (C) The most probable phase difference (shown by dashed line in A) is shown for three values of α. In the presence of noise (α ≠ 0) the most probable phase difference is different from the fixed point of the deterministic equations (black curve α = 0).
Mentions: Figure 2A shows the steady state phase difference distribution for different values of the frequency mismatch for QIF neuronal oscillators. It can be seen that the distribution becomes narrower (with a more pronounced peak) with increasing frequency mismatch while the neurons remain in 1:1 locked state, i.e. for the mismatch in the range . This reflects a larger basin of attraction for the locked state when mismatch is increased from zero. Most robust locking occurs for when the basin of attraction is symmetric around the stable fixed point. Furthermore, the asymmetry of the basin of attraction causes the distribution of the phase differences not to peak in the fixed point of the deterministic equation, determined by . In turn, in presence of noise the location of maximum phase difference satisfies,which is derived by taking the derivative of ρ(ϕ) with respect to ϕ, equal to zero. The location of the most probable phase difference as a function of mismatch, determined by Eq. (7), is plotted in Fig. 2C for different values of the noise amplitude as well as for the noiseless system which coincides with the location of the fixed point. Presence of noise inclines the distribution to larger phase differences for small values of frequency mismatch. The maximum difference between the location of most probable phase difference between noiseless state and noisy state is seen near which reflects the most asymmetric basin of attraction for the locked state and in turn the locations coincide when ϕ* = π/2 where the basin of attraction is symmetric.

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