Noises- and delay-enhanced stability in a bistable dynamical system describing chemical reaction

Abstract

In this paper, we consider the Schlogl model with time-delayed feedback to study the switching behavior of a bistable chemical reaction system in the presence of cross-correlated multiplicative and additive noise sources. Our results show that (i) the multiplicative noise (or additive noise) can induce the switch from high (or low) concentration state to low (or high) concentration one; (ii) the mean first passage time (MFPT) of switch from high concentration state to the low concentration one as functions of the noise strengths exhibits a maximum, which is the signature of the noise enhanced stability (NES) phenomenon for the high concentration state; and (iii) as the value of cross-correlation strength λ, time delay τ, or strength K of the feedback loop increases, the maximum in the MFPT increases, i.e., λ, τ, or K can enhance stability of the high concentration state.