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    <title>Physiologically motivated multiplex Kuramoto model describes phase diagram of cortical activity</title>
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    <abstract>We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of  interconnected cortical regions. This is mathematically possible due to the existence of a unique, stable limit cycle, weak coupling, and  inhibitory synaptic time delays. We study the phase diagram of this model numerically as a function of the inter-regional connection strength that  is related to cerebral blood flow, and a phase shift parameter that is associated with synaptic GABA cncentrations. We find three macroscopic phases of cortical activity: background activity (unsynchronized oscillations), epileptiform activity (highly synchronized oscillations) and resting-state activity (synchronized clusters/chaotic behaviour). Previous network models could hithero not explain the existence of all three  phases. We further observe a shift of the average oscillation frequency towards lower values together with the appearance of coherent slow  oscillations at the transition from resting-state to epileptiform activity. This observation is fully in line with experimental data and could explain the  influence of GABAergic drugs both on gamma oscillations and epileptic states. Compared to previous models for gamma oscillations and  resting-state activity, the multiplex Kuramoto model not only provides a unifying framework, but also has a direct connection to measurable  physiological parameters.</abstract>
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