On the efficiency of pairwise Hamiltonian control to desynchronize the higher-order Kuramoto model

TL;DR

This paper investigates how pairwise Hamiltonian control can effectively desynchronize higher-order Kuramoto models, revealing that higher-order interactions influence control efficiency and that a sufficient number of controlled nodes can achieve desynchronization.

Contribution

It introduces a minimally invasive pairwise control method based on Hamiltonian control theory for higher-order Kuramoto models, analyzing its effectiveness under various interaction strengths.

Findings

Higher-order interactions increase the difficulty of desynchronization near synchronization.

Intermediate higher-order interaction strengths hinder desynchronization, larger ones facilitate it.

Control effectiveness depends on the number of controlled nodes and interaction strength.

Abstract

Synchronization of coupled oscillators is observed in many natural and engineered systems and emerges due to the interactions within the system. It can be both beneficial, e.g., in power grids, and harmful, e.g., in epileptic seizures. In the latter case, efficient control methods to desynchronize the systems are crucial. Recent studies have shown that interactions are not always pairwise, but higher-order, i.e., many-body, and this greatly affects the dynamics. For instance, higher-order interactions increase the linear stability of synchronized states but simultaneously shrink their attraction basin, with potentially opposite effects on control methods. Here, we use a minimally invasive pairwise control based on Hamiltonian control theory, and investigate its efficiency on phase oscillators with higher-order interactions. We show that, if the initial phases are close to the synchronized state, higher-order interactions make desynchronization more difficult to achieve. Otherwise, a non-monotonic effect appears: intermediate strengths of higher-order interactions impede desynchronization while larger ones facilitate it. In all cases, the control can desynchronize the system with a sufficient number of controlled nodes and intensity.