Hebbian plasticity rules abrupt desynchronization in pure simplicial complexes

TL;DR

This paper explores how Hebbian-like adaptive coupling in pure simplicial complexes induces abrupt, first-order desynchronization transitions in oscillator networks, supported by mean-field analysis and numerical simulations.

Contribution

It introduces a novel adaptive simplicial complex model with Hebbian rules, revealing first-order desynchronization transitions in oscillator ensembles.

Findings

Adaptive coupling leads to abrupt desynchronization.

Transitions are governed by Hebbian learning parameters.

Mean-field analysis aligns with numerical results.

Abstract

This Letter investigates the upshots of adaptive development of pure 2- and 3- simplicial complexes (triad and tetrad) on the nature of the transition to desynchrony of the oscillator ensembles. The adaptation exercised in the pure simplicial coupling takes a cue from the Hebbian learning rule, i.e., the coupling weight of a triad (tetrad) is prone to increase if the oscillators forming it are in phase and decrease if they are out of phase. The coupling weights in these pure simplicial complexes experiencing such adaptation give rise to first-order routes to desynchronization, whose onsets are entirely characterized by respective Hebbian learning parameters. Mean-field analyses presented for the order parameters for the adaptive 2- and 3- simplicial complexes strongly corroborate with the respective numerical assessments.