LAUSR

Scattering processes are typically sensitive to the incident wave properties and to interference effects generated via wave-matter interactions with the target. We challenge this general belief in the case of targets that undergo time-periodic modulations encircling quasiadiabatically an exceptional point in a given parameter space. When the scattering dwell time is above a critical value τ_{c}, the scattered field is surprisingly insensitive to the properties of the incoming wave and local operational details of the driving. Instead, it reaches a fixed point attractor that can be controlled by the direction of the driving cycle. For dwell times below τ_{c}, the unusual robustness is abruptly suppressed. Such protocols may become useful tools in control engineering, including the management of thermal and quantum fluctuations.