Metastability induced by non-reciprocal adaptive couplings in Kuramoto models

TL;DR

This paper investigates how non-reciprocal adaptive couplings in generalized Kuramoto models induce metastability, resembling brain dynamics, through deterministic mechanisms that cause oscillators to switch clusters over time.

Contribution

It introduces a novel analysis of metastability caused by non-reciprocal adaptive couplings in Kuramoto models, linking deterministic dynamics to brain-like switching behavior.

Findings

Metastability depends on system size and network connectivity.

Oscillator cluster switching creates weak ties between synchronized groups.

Deterministic dynamics produce random-like time series.

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 metastability 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 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. The time series exhibit random features but arise from deterministic dynamics.