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Two-dimensional Fourier transform as a tool for identification of coherent patterns in spiking neuronal networks
Identification of coherent states of spiking neural networks is a fundamental problem of
synchronization theory but conventional methods are computationally expensive. We apply
the crystallographic ideas of processing periodic structures to the analysis of various
states of spiking neuronal networks. In particular, the introduced approach is based on
the application of two-dimensional Fourier transform to rasterplots. By the position of the
peaks in the reciprocal space, the approach makes it possible to identify the state of spiking
neuronal networks and to determine its properties such as spike activity frequencies
for global and clusters synchronization state, the propagation velocity of traveling waves.
The approach also allows to identify static and traveling chimera states and to determine
their properties, including the propagation velocity of traveling chimera, after separating
coherent and incoherent chimera domains, and applying the two-dimensional Fourier
transform to the chimeric part separately. The approach does not require high-resolution
time series of membrane potentials of neurons and large computational resources; moreover,
it is acceptable to feed just 8-bit images to the input of the algorithm making it
applicable in the context of experimental neuroscience, where access to raw time-series
data may be limited or unavailable.