Collective dynamics of coupled oscillator networks subjected to external forcing*

Many natural and engineered flows behave as complex systems, characterized by collective phenomena emerging from interactions among their constituent parts. Such collective behavior, while difficult to predict through reductionist analysis, can offer practical benefits. We investigate oscillation quenching and synchronization in networks of Stuart-Landau oscillators interacting via time-delay coupling. By systematically varying the network topology and coupling parameters, we identify multiple collective states, including amplitude death, chimeras, and in-phase/anti-phase synchronization. Specifically, we find that amplitude death occurs most readily in ring networks with an odd number of non-identical oscillators. We further explore the combined effects of mutual coupling and external forcing by introducing time-periodic excitation of varying amplitudes and frequencies. Our results reveal that external forcing is more effective at weakening the self-excited oscillations in chain and star networks compared to ring networks. This research provides insights into the synergistic use of mutual coupling and external forcing to achieve specific collective states in networks of coupled limit-cycle oscillators, with potential applications in flow control and network dynamics.