Stochastic Delay Kinetics Study In DM Surface Reaction System

In recent years, with the object of chemical study to complex systems, such as surface catalytic system, etc. Research of nonlinear dynamics problem of complex system attracts widely attention. These systems have a high degree of complexity, inevitably affected by intrinsic and extrinsic fluctuations (noise) and time delay. The combination of noise and time delay is ubiquitous in nature, and often change fundamentally dynamical behavior of the system, and make the systems produce more richer and complex dynamical behaviors. At present, theoretical studies of the nonlinear dynamics properties, mostly introduce the macroeconomic deterministic or stochastic dynamic equation, and rarely take into account the time delay factor, especially the impact of combination of noise and time delay on complex systems. Thus, study of the character, mechanism and application have important realistic significance and scientific value. This paper choose surface catalytic system for the object of research, and discuss the impact of noise and time delay on the dynamical behaviors of the system, as well as the regulative effect of the noise correlation on the complex systems.This paper firstly introduce the knowledge of the background involved in paper, such as Dimer-Monomer reaction model(DM model), considering various dimer adsorption mechanisms in catalyst surface, namely, local and random adsorption surface catalytic reaction models. Then we elaborate stochastic delayed theory associated with this paper and the extension, including the analytical approximation and numerical simulation of complex systems under the action of noise and time delay. Second, we consider the effects of noise and time-delayed feedback in the surface catalytic reaction model, the surface catalytic reaction of carbon monox-ide as a prototype, we use site approximation in mean-field theory to study first-and second-order non-equilibrium phase transition (PT, generalized phase tran-sition) of the DM model. Based on dimer local adsorption model, we construct a stochastic delayed differential equation and its Fokker-Planck equation to describe the state evolution of the DM reaction model. We show that the noise can only induce first-order IPT characteristic of the DM model, however the combination of the noise and time-delayed feedback can simultaneously induce first-and second-order non-equilibrium PT characteristics of the DM model. Therefore, considering the effects of noise and time delay, the theoreti-cal prediction values (Ys1=0.389and YS2=0.5175) of first-and second-order non-equilibrium PT of the DM model are good agreement with the recent exper-imental simulation values (Y1=0.389±0.005and Y2=0.525±0.001). In this sense say, the well-known first-and second-order PT characteristics of the DM model may be viewed as noise-and delay-induced non-equilibrium dynamical phase transitions.Third, we consider the effects of noise and time-delayed feedback in the DM surface reaction model. Applying small delay approximation, we obtain the the stationary probability distribution(SPD). Based on the extreme of SPD, we discuss the effects of the noise and time-delayed feedback on the non-equilibrium dynamical phase transition. It is shown that, for the local adsorption surface catalytic reaction model (i.e., two spinodal points exist at yis1(?)0.3874and yls2(?)0.5182), and for random adsorption surface catalytic reaction model, two spinodal points exist at yrs1(?)0.3874and yrs2(?)0.5260, which is in good agreement with the experimental MCS of the first-and second-order non-equilibrium IPTs(i.e., y1=0.3873682±0.0000015?y2=0.525615±0.000005), respectively. Therefore the qualitative predictions of the first-and second-order non-equilibrium PTs are better for the random adsorption surface catalytic reaction model than that for the local adsorption surface catalytic reaction model.Finally, we consider the surface catalytic reaction system including in-trinsic and extrinsic noises, and obtain delayed Langevin equation. Based on the delayed Fokker-Planck equation, calculating characteristic parameters of the non-equilibrium phase transition behavior(the extreme of the steady state probability distribution), analyzing the effect mechanism of noises and their correlation on the non-equilibrium phase transition. This results show that: the external noise and noise correlation cause contraction of the reactive win-dow width. The impact of the internal noise on the behavior of non-equilibrium dynamical phase transition depends on the noise correlation, i.e., when the two noise negative correlation, the internal noise causes expansion of the reactive window width. However when the two noise positive correlation, the internal noise causes contraction of the reactive window width. Therefore, the noise-caused changes of reaction window have important scientific significance.