brainpy.measure.voltage_fluctuation
brainpy.measure.voltage_fluctuation#
- brainpy.measure.voltage_fluctuation(potentials)[source]#
Calculate neuronal synchronization via voltage variance.
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
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.