Metastability induced by non-reciprocal adaptive couplings in Kuramoto models

Abstract: Non-reciprocal couplings are frequently found in systems out-of-equilibrium such as neuronal networks. We consider generalized Kuramoto models with non-reciprocal adaptive couplings. The non-reciprocity refers to the type of couplings according to Hebbian or anti-Hebbian rules and to different time scales, on which the couplings evolve. The main effect of this specific combination of deterministic dynamics is an induced metastability of anti-phase synchronized clusters of oscillators. Metastable switching is typical for neuronal networks and a characteristic of brain dynamics. We analyze the metatstability as a function of the system parameters, in particular of the size and the network connectivity. The mechanism behind sudden changes in the order parameters are individual oscillators which change their cluster affiliation from time to time, providing ``weak ties" between clusters of synchronized oscillators. The time series have random features, but derive from deterministic dynamics.