A runner loses on both a smooth track and sticky sand. Seems hopeless. But if the surface underfoot starts changing every few seconds (track, then sand) the runner suddenly stops falling behind. He doesn't get faster; the environment just doesn't get a chance to 'crush' his weakness.
That's exactly what the authors found when studying a simple predator–prey model. They took a predator that inevitably goes extinct in two constant environments (say, a cold climate and a hot one). But when they started switching the environment back and forth, the predator survived. The key is speed: the switches must be frequent enough. If you delay the switch, the predator will go extinct during the unfavorable phase. The researchers derived a critical frequency — the very tempo above which salvation occurs.
This is not just a mathematical curiosity. The authors generalized the finding to any two-species system and obtained a simple criterion — the 'rescue switching function.' Just take two descriptions of the environment (their 'vector fields') and compute the sign of this function. If it's positive — switching saves the species. If negative: it doesn't. Applying this to a viral infection model, the scientists showed that two drugs, each of which alone kills the virus, can fail if alternated. The virus doesn't have time to develop resistance: it's saved by the very rhythm of drug switching.
In nature, this effect might explain why some rare species persist in places with variable climates, even though in stable zones they would be outcompeted.
In the movie 'Interstellar,' the crew searches for a planet where time flows differently — here, the very 'breathing' of the environment turns out to be more important than its properties.