Effects of Time Delay on Resonant Activation over a Fluctuating Barrier Driven by Correlated Noises

The time delay effects on the mean first passage time (MFPT) of a particle over a fluctuating potential barrier in the presence of correlated noises are investigated. It is shown that the MFPT displays the resonant activation (RA) phenomenon which can be enhanced by time delay feedbacks. In the non-delayed case, with increasing noise correlation intensity, RA is strengthened. However, under the synergistic reaction of time delay and noise correlation, there is a critical behavior which distinguishes resonant activation from resonant restraint at the corresponding critical value lambda = 0.02, which is a so-called critical phenomenon.