Our research group DRIFT (Dynamics of Rate Induced and Fading in Time systems) was initiated at the Budapest University of Technology and Economics in 2026, after earning an ADVANCED research grant provided by the National Research, Development and Innovation Office of Hungary. We aim to investigate the general properties of chaotic transients in explicitly time-dependent and purely decaying dynamical systems. Our investigations will reach open questions in a variety of engineering and scientific disciplines, ranging from the rocking dynamics of free standing buildings under earthquake-like effects, through shape evolution of rocks under abrasion, to the transport of runaway electrons tokamaks like the ITER experimental fusion reactor. We also challenge our methods by investigating time-varying stellar systems, and stability of nuclear reactors. We anticipate that the results achieved by the synergy of our project can contribute to public safety against earthquakes, and to greener energy production using stable performance of fission and fusion energy production in the future.