External and internal factors may cause a system’s parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a time-delayed oscillator whose time delay varies at a small but non-negligible rate. Our research shows that due to this parameter drift, trajectories from a chaotic attractor tip to other states with a certain probability. This causes the appearance of the phenomenon of transient chaos. By using an ensemble approach, we find a gamma distribution of transient lifetimes, unlike in other non-delayed systems where normal distributions have been found to govern the process. Furthermore, we analyze how the parameter change rate influences the tipping probability, and we derive a scaling law relating the parameter value for which the tipping takes place and the lifetime of the transient chaos with the parameter change rate.

外部和内部因素可能会导致系统参数在稳定之前随时间变化。当参数越过分叉点时，这种漂移会引起状态偏移。在这里，我们研究一个无限维系统的情况：一个时滞振荡器，其时延以很小但不可忽略的速率变化。我们的研究表明，由于该参数漂移，从混沌吸引子尖端到其他状态的轨迹具有一定的概率。这导致出现瞬时混乱现象。通过使用集成方法，我们发现了瞬态寿命的伽马分布，这与其他非延迟系统不同，在该非延迟系统中，正态分布已决定了该过程。此外，我们分析了参数变化率如何影响倾翻概率，