Impact of higher-order interactions on aging transition in fractional-order coupled oscillator networks

As the proportion of inactive or damaged oscillators increases, coupled oscillator systems may undergo a transition to the macroscopically inactive state, known as aging transition (AT). The loss of macroscopic oscillations caused by the process of AT could lead to a profound impact on the rhythmic activities of some physical and biological systems. Yet, it is still unclear under which conditions AT will occur in the face of both fractional-order derivative and higher-order interactions. In this work, we construct the simplicial complexes from Erdős–Rényi networks and incorporate the higher-order interactions into a system of fractional-order Stuart–Landau oscillators. Through theoretical analysis, we derive the critical fraction of inactive oscillators required for the onset of AT, and the analytical predictions are further validated by extensive numerical simulations. Our results demonstrate that both the fractional-order derivative and higher-order interactions facilitate the occurrence of AT. Moreover, under specific parameter regimes, a partial amplitude death state is also observed. These findings shed new light on the design principles of robust complex systems in which memory effects and multi-body interactions are intrinsically intertwined.