# brainpy.measure.voltage_fluctuation#

brainpy.measure.voltage_fluctuation(potentials)[source]#

Calculate neuronal synchronization via voltage variance.

The method comes from 1 2 3.

First, average over the membrane potential $$V$$

$V(t) = \frac{1}{N} \sum_{i=1}^{N} V_i(t)$

The variance of the time fluctuations of $$V(t)$$ is

$\sigma_V^2 = \left\langle \left[ V(t) \right]^2 \right\rangle_t - \left[ \left\langle V(t) \right\rangle_t \right]^2$

where $$\left\langle \ldots \right\rangle_t = (1 / T_m) \int_0^{T_m} dt \, \ldots$$ denotes time-averaging over a large time, $$\tau_m$$. After normalization of $$\sigma_V$$ to the average over the population of the single cell membrane potentials

$\sigma_{V_i}^2 = \left\langle\left[ V_i(t) \right]^2 \right\rangle_t - \left[ \left\langle V_i(t) \right\rangle_t \right]^2$

one defines a synchrony measure, $$\chi (N)$$, for the activity of a system of $$N$$ neurons by:

$\chi^2 \left( N \right) = \frac{\sigma_V^2}{ \frac{1}{N} \sum_{i=1}^N \sigma_{V_i}^2}$
Parameters

potentials – The membrane potential matrix of the neuron group.

Returns

sync_index – The synchronization index.

Return type

float

References

1

Golomb, D. and Rinzel J. (1993) Dynamics of globally coupled inhibitory neurons with heterogeneity. Phys. Rev. reversal_potential 48:4810-4814.

2

Golomb D. and Rinzel J. (1994) Clustering in globally coupled inhibitory neurons. Physica D 72:259-282.

3

David Golomb (2007) Neuronal synchrony measures. Scholarpedia, 2(1):1347.