Mean first-passage time in a delayed tristable system driven by correlated multiplicative and additive white noises

This paper investigates the mean first-passage times (MFPTs) of a delayed tristable system driven by correlated multiplicative and additive noises. The results suggest that the correlation between the multiplicative and additive noises can induce symmetry-breaking in the delayed tristable system. The noise-induced dynamics, such as the noise enhanced stability (NES) and the resonant activation (RA), can be observed with considering the combined influences of correlated noises and intermediate stable state. The time delay plays an important role in the MFPTs. For example, with respect to the middle well, the increase of time delay results in the weakening of the stability of the two lateral wells; thus, all the MFPTs are decreased notably. Moreover, a law of MFPTs is established for three different potential wells. That is, the MFPT T(s₁ → s₃) (between the left and right wells) is equal to the sum of T(s₁ → s₂) (from left well to middle one) and T(s₂ → s₃) (from middle well to right one). However, this change regulation can be first broken with an increase in time delay, and then restored with the increase of correlation between noises.