Effects of Time Delay on the Bistable System Subjected to Correlated Noises

The time-delayed bistable system subjected to the multiplicative and additive noises is investigated. In the condition of small delay time, the stationary probability distribution function (SPDF) is derived, and under the condition of large delay time, the SPDF is stochastically simulated. The analytical and
simulative results indicate that: (i) For the case of λ=0 (λ denotes the strength of correlations between the multiplicative and additive noises), the time delay affects weakly the SPDF peak structure, and the symmetrical
property of the SPDF two-peak structure does not change with the increasing delay time. (ii) For the case of λ≠0, the two-peak structure changes with the increasing delay time, i.e. one peak goes up and the other go down simultaneously as the delay time increases and along with further increase of the delay time, the lower peak disappears gradually while the higher one goes up, i.e. the structure of the SPDF changes from a bimodal to a unimodal and the system becomes monostable.