Impact of higher-order interactions on amplitude death of coupled oscillators

Extensive studies of coupled dynamical systems have shown that under certain underlying interactions, all the individual subsystems may cease totally their intrinsic oscillations and are stabilized to a homogeneous steady state, which is known as amplitude death (AD). The presence of higher-order many-body interactions can overcome the limitation of first-order pairwise interactions, and more vividly model the emergent dynamics in real-world systems. However, it is still unclear whether and under which conditions AD can be achieved in the presence of higher-order interactions. In this work, by considering a simplicial complex of coupled Stuart–Landau oscillators, we investigate the impacts of first-order (pairwise) and second-order (three-body) interactions on the emergence of AD dynamics. The results show clear evidence that the higher-order interactions can facilitate the onset of AD dynamics with a lower coupling strength. In particular, we first derive the necessary condition to determine the onset of AD by performing linear stability analysis. Then we show, via numerical simulations, that AD can be achieved by either first-order or second-order interactions only, and the required coupling strength of first-order interactions is much higher than the second-order ones. Finally, we conclude that the physical mechanism is due to the reflection of interaction units between oscillators, that is, the network with second-order interactions allows the nodes to involve more interactions simultaneously than the one with first-order interactions. These results shed a new insight into the generation of AD phenomenon and reveal that the higher-order interactions can serve as a rather efficient approach to quench the rhythmic activities.