  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.
