In recent years, with the development of chemical study of complex systems, such as surface catalytic system, etc. the research of nonlinear dynamics problem of complex system has received much attention. These systems have high-degree complexity, and they are inevitably affected by intrinsic and extrinsic fluctuations (noise) and time delay. The combination of noise and time delay is ubiquitous in nature, and often changes fundamentally dynamical behavior of the system, and thus making the system produce more richer and complex dynamical behaviors. At present, in the theoretical studies of the nonlinear dynamic properties, the macroeconomic deterministic or stochastic dynamic equation is adopted most, and the time delay factor, especially the influences of combination of noise and time delay on complex system are rarely taken into account. Thus, the study of the character, mechanism and application has important realistic significance and scientific value. In this paper, we first introduce the Dimer-Monomer reaction model (DM model), where various dimer adsorption mechanisms in catalyst surface, namely, the local and random adsorption surface catalytic reaction models are considered. Then we use the stochastic delayed theory involved in this paper and its extension, including the analytical approximation and numerical simulation of complex systems under the action of noise and time delay. In this paper, we consider the effects of noise and time-delayed feedback in the surface catalytic reaction model, and construct a delayed monomer-dimer surface reaction model including correlated noise. According to the Langevin equation, applying small delay approximation, we obtain the delayed Fokker-Planck equation for calculating characteristic parameters of the non-equilibrium phase transition behavior (the extreme of the steady state probability distribution), analyzing the effect mechanism of noise and its correlation with the non-equilibrium phase transition. The MD model exhibits the first- and second-order phase transition, namely, the reactive window between first- and second-order phase transition. The MD models for various dimer adsorption mechanisms (namely, local and random adsorption models) are discussed. The results are indicated as follows. (1) The external noise and correlation between two noise signals cause the reactive window width to contract. (2) The influence of the internal noise on the behavior of non-equilibrium dynamical phase transition depends on the noise correlation, i.e., when the two noise signals are negatively correlated, the internal noise causes the reactive window width to expand. However when the two noise signals are positively correlated, the internal noise causes the reactive window width to contract. (3) The noise-caused changes of reaction window have important scientific significance in the first- and second-order phase transition of the MD surface reaction model.