Amplitude death in time-delay-coupled Stuart-Landau oscillators via dissipative coupling and frequency detuning

Flows in natural and technological systems often exhibit collective behavior emerging from the nonlinear interactions among their constituent elements. Predicting such behavior is challenging, yet harnessing it offers practical advantages for flow control. Here, we explore amplitude death in networks of Stuart-Landau oscillators under varying coupling conditions. For pure time-delay coupling, we build two-parameter dynamical maps (delay time vs coupling strength) for ring, chain, and star networks, revealing regimes of synchronization and amplitude death. Introducing dissipative coupling enlarges the amplitude-death zones and suppresses competing dynamical states. Introducing frequency detuning in time-delay-coupled networks (without dissipative coupling) enlarges the amplitude-death zones in proportion to the detuning ratio, most notably in chain and star networks at low coupling strengths. These findings demonstrate a complex interplay among the coupling properties, network topology, and frequency detuning, providing useful guidelines for passive control of flow-oscillator networks.