Hebbian plasticity assisted robust desynchronization in simplicial complexes.

The plasticity in higher-order coupling interaction, best encoded by an adaptive simplicial complex structure, may significantly affect the synchronization dynamics. Here, we investigate the impact of adaptation in the 2-simplex (triadic) coupling on the nature of the transition to desynchrony in the networked oscillators. The adaptation in triadic coupling takes a cue from the Hebbian learning rule, i.e., the coupling weight of a triad is prone to increase if the oscillators forming the triad are in phase and decrease if they are out of phase. The triadic coupling weights adapting through the Hebbian learning mechanism give rise to a first-order route to desynchronization as observed in the case of static triadic coupling; however, its onset is entirely regulated by the Hebbian learning parameters. The fact that the Hebbian learning parameters govern the onset of desynchronization is supported by rigorous mean-field analysis.