Clustering and synchronization in phase models with state dependent coupling

We study a class of coupled phase models with state-dependent coupling topology. In these models the link weights increase (decrease) in a dynamic fashion according to the phase differences of the coupled systems. We provide sufficient conditions for the systems to be gradients of suitable potential functions and we analyze their clustering properties. The work is motivated by neurophysiological models where the strength of the synapse between two neurons is enhanced if they are simultaneously co-active (close to synchronization) and decreased when they are out of phase.