  Rate-induced tipping occurs when a ramp parameter changes rapidly enough to
cause the system to tip between co-existing, attracting states. We show that
the addition of noise to the system can cause it to tip well below the critical
rate at which rate-induced tipping would occur. Moreover it does so with
significantly increased probability over the noise acting alone. We achieve
this by finding a global minimizer in a canonical problem of the
Freidlin-Wentzell action functional of large deviation theory that represents
the most probable path for tipping. This is realized as a heteroclinic
connection for the Euler-Lagrange system associated with the Freidlin-Wentzell
action and we find it exists for all rates less than or equal to the critical
rate. Its role as most probable path is corroborated by direct Monte Carlo
simulations.
