  We investigate delay effects on dominant transition pathways (DTP) between
metastable states of stochastic systems. A modified version of the Maier-Stein
model with linear delayed feedback is considered as an example. By a stability
analysis of the {"on-axis"} DTP in trajectory space, we find that a bifurcation
of DTPs will be induced when time delay $\tau$ is large enough. This finding is
soon verified by numerically derived DTPs which are calculated by employing a
recently developed minimum action method extended to delayed stochastic
systems. Further simulation shows that, the delay-induced bifurcation of DTPs
also results in a nontrivial dependence of the transition rate constant on the
delay time. Finally, the bifurcation diagram is given on the $\tau-\beta$
plane, where $\beta$ measures the non-conservation of the original Maier-Stein
model.
