Gamma --> beta frequency shift in the circuits with strongly facilitating synapses.

Synapses exhibiting strong elevation of postsynaptic response due to paired pulse stimulus have been reported in literature [1]. Hereby we investigate the role of strongly facilitating synapses [1] in neural circuits. Using the non-linear short term facilitaion model presented in [2] and formalism developed in [3], we derive a Wilson-Cowan model of strongly facilitating synapse. Then we investigate the possible role of excitatory strong facilitating synapse [1,2] between the excitatory and inhibitory population, showing that it can play an important role in beta --> gamma frequency shift and possible generation of beta rebound, that can be seen in Figure below.
[1] Thomson AM. Journal of Physiology 1997
[2] Jędrzejewska-Szmek J, Michalski A, Żygierewicz J. BMC Neuroscience 2011
[3] Tsodyks MV, Pawelzik K, Markram H. Neural Computation 1998