Correlated noise induced non-equilibrium phase transition in surface catalytic reaction model

Liu Rui-Fen; Hui Zhi-Xin; Xiong Ke-Zhao; Zeng Chun-Hua

doi:10.7498/aps.67.20180250

Abstract

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.

Keywords:

Authors and contacts

1.
Institute of Physical and Engineering Science, Kunming University of Science and Technology, Kunming 650500, China;
2.
School of Physics and Electronic Information Engineering, Ningxia Normal University, Guyuan 756000, China;
3.
Department of Physics, East China Normal University, Shanghai 200062, China

Corresponding author: Zeng Chun-Hua, zchh2009@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11665014), the Natural Science Foundation of Yunnan Province, China (Grant No. 2017FB003), the Candidate Talents Training Fund of Yunnan Province, China (Grant No. 2015HB025), the Natural Science Foundation of Ningxia, China (Grant No. NZ17255), and the Scientific Research Foundation of the Higher Education Institutions of Ningxia, China (Grant No. NGY2016194).

References

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Cited By

[1]	Xin H W, Hou Z H 2009 Nonlinear Chemistry (Hefei: University of Science and Technology of China Press) pp1-10 (in Chinese) [辛厚文, 候中怀 2009 非线性化学 (合肥: 中国科学技术大学出版社) 第1–10页]
[2]	Zeng C H 2014 Ph. D. Dissertation (Kunming: Kunming University of Science and Technology) (in Chinese) [曾春华 2014 博士学位论文(昆明: 昆明理工大学)]
[3]	Hu G, Ditzinger T, Ning C Z, Haken H 1993 Phys. Rev. Lett. 71 807
[4]	Bao J D, Zhuo Y Z 2003 Phys. Rev. Lett. 91 138107
[5]	Glansdorff P, Prigogine I 1971 Thermodynamic Theory of Structure, Stability and Fluctuations (New York: Wiley-Interscience) pp21-50
[6]	Yu W, Zhang J, Tang J 2017 Acta Phys. Sin. 66 200201 (in Chinese) [于文婷, 张娟, 唐军 2017 物理学报 66 200201]
[7]	Jia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[8]	Ai B Q, Wang X J, Liu GT, et al. 2003 Phys. Rev. E 67 022903
[9]	Hou Z, Xin H 2003 J. Chem. Phys. 119 11508
[10]	Hou Z, Yang L, Xin H 1998 Surface Sci. 399 L332
[11]	Suchorski Y, Beben J, James E W, et al. 1999 Phys. Rev. Lett. 82 1907
[12]	Sachs C, Hildebrand M, Volkening S, et al. 2001 Science 293 1635
[13]	Peskov N V, Slinko M M, Jaeger N I 2002 J. Chem. Phys. 116 2098
[14]	Zhao G, Hou Z H, Xin H W 2005 J. Phys. Chem. A 109 8515
[15]	Zhao N, Luo J 2001 J. Chem. Phys. 114 7761
[16]	Luo J, Zhao N, Hu B 2002 Phys. Chem. Chem. Phys. 4 4149
[17]	Hayase Y, Wehner S, Kuppers J, Brand H R 2004 Phys. Rev. E 69 021609
[18]	Pineda M, Imbihl R, Schimansky-Geier L 2007 Phys. Rev. E 75 061107
[19]	Pineda M, Toral R 2009 J. Chem. Phys. 130 124707
[20]	Pineda M, Imbihl R, Schimansky-Geier L 2010 Physica A 389 1178
[21]	Cisternas J, Lecaros R, Wehner S 2011 Eur. Phys. J. D 62 91
[22]	Fulinski A, Telejko T 1991 Phys. Lett. A 152 11
[23]	Zhou R W, Li J C, Dong Z W, et al. 2017 Acta Phys. Sin. 66 040501 (in Chinese) [周若微, 李江城, 董志伟, 等 2017 物理学报 66 040501]
[24]	Madureira A J R, Hänggi P, Wio H S 1996 Phys. Lett. A 217 248
[25]	Zeng C, Zeng J, Liu F, Wang H 2016 Sci. Reports 6 19591
[26]	Shit A, Chattopadhyay S, Banik S K, Chaudhuri J R 2010 Chaos 20 023130
[27]	Tessone C J, Wio H S, Hänggi P 2000 Phys. Rev. E 62 4623
[28]	Jia Y, Yu S N, Li J R 2000 Phys. Rev. E 62 1869
[29]	Zeng C, Zhou X, Tao S 2009 J. Phys. A: Math. Theor. 42 495002
[30]	Zeng C, Wang H 2010 J. Stat. Phys. 141 889
[31]	Zeng C, Gong A, Tian Y 2010 Physica A 389 1971
[32]	Zeng C H, Wang H, Nie L R 2012 Chaos 22 033125
[33]	Zeng C H, Wang H, Nie L R 2012 Chaos 22 039901
[34]	Liu Q, Jia Y 2004 Phys. Rev. E 70 041907
[35]	Zhang X D, Yang X Q, Tao Y 2011 Plos One 6 17104
[36]	Ghosh S, Banerjee S, Bose I 2012 Eur. Phys. J. E 35 11
[37]	Zeng C, Han Q L, Yang T, Wang H, Jia Z L 2013 J. Stat. Mech. 2013 P10017
[38]	Duan W, Zeng C 2017 Appl. Math. Comput. 292 400
[39]	Duan W, Zeng C 2017 Appl. Math. Comput. 293 611
[40]	Zeng C, Wang H 2012 Chem. Phys. 402 1
[41]	Zeng C, Wang H, Yang T, et al. 2014 Eur. Phys. J. B 87 137
[42]	Ziff R M, Gulari E, Barshad Y 1986 Phys. Rev. Lett. 56 2553
[43]	Dickman R 1986 Phys. Rev. A 34 4246
[44]	Tammaro M, Evans J W 1995 Phys. Rev. E 52 2310
[45]	Turanyi T, Tomlin A, Pilling M 1993 J. Phys. Chem. 97 1674
[46]	Bennett M R, Volfson D, Tsimring L, Hasty J 2007 Biphys. J. 92 3501
[47]	Pineda M, Toral R 2009 J. Chem. Phys. 130 124707
[48]	Frank T D 2005 Phys. Rev. E 71 031106
[49]	Frank T D 2005 Phys. Rev. E 72 011112
[50]	Gitterman M 1999 J. Phys. A 32 L293
[51]	Berdichevsky V, Gitterman M 1999 Phys. Rev. E 60 1494

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Vol. 67, Issue 16 - 2018-08-20

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