Amplitude Death in a Ring of Nonlinear Oscillators with Unidirectional Coupling

It has been widely studied that the interaction among subsystems can lead to the collective behavior such as synchronization and amplitude death. Among these collective behaviors in coupled oscillators, the amplitude death refers to a situation where individual oscillators cease to oscillate when they are coupled, which is a useful control mechanism for stabilizing systems to steady states. Most of the previous studies on amplitude death have dealt with bidirectional coupling cases. Here, we studied the amplitude death in a ring of coupled nonlinear oscillators with unidirectional couplings and discuss the differences between amplitude death behavior in unidirectional and bidirectional coupling cases.