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. Via bifurcation analysis and numerical integration 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. The time series exhibit random features but arise from deterministic dynamics. We analyze the metastability as a function of the system parameters, in particular of the size and the network connectivity. Metastable switching is typical for neuronal networks and a characteristic of brain dynamics. The mechanism behind the observed sudden changes in the order parameters is individual oscillators which change their cluster affiliation from time to time, providing "weak ties" between clusters of synchronized oscillators, where an individual oscillator may represent an entire brain area. This mechanism provides an alternative way of inducing metastability in the oscillatory system to switching events as result of heteroclinic dynamics.