The maximal likelihood transition path(MLP)is informative to explain the
mechanism of the noise-induced transition, such as chemical reactions,
biological switches, nucleation processes, etc. In present paper, we
investigate the MLP between two metastable states in a delayed stochastic
system by employing a recently developed minimum action method. A modified
version of the Maier-Stein model with linear delayed feedback is considered as
an example.