The nonequilibrium phase transition and the symmetry revival induced by time delay in an asymmetric bistable system with correlated noises

The nonequilibrium phase transition and the symmetryrevival induced by time delay in a bistable system are investigated.The stationary probability distribution function (SPDF) of thebistable system with time delay and correlated noises are calculatedby an analytical method and stochastic simulation respectively. Theanalytical and simulative results indicate that: (1) There is acertain value of λ (λ denotes the strength ofcorrelations between the multiplicative and additive noises) to makethe SPDF symmetric under some time delay; however, above or belowthe given value, the symmetry will be broken; (2) With themonotonic change of λ , the unimodal peak structure of SPDFbecomes bimodal at the beginning, then it becomes unimodal again; thismeans that there is a reentrance phenomenon in the process; (3)There is a critical value of delay time, which makes the lower peakof SPDF equal to the higher one under the critical condition. Thismeans that the symmetry revival phenomenon emerges.