社交网络中信息传播的稳定性研究

王超; 刘骋远; 胡元萍; 刘志宏; 马建峰

doi:10.7498/aps.63.180501

摘要

社交网络已成为当前最重要的信息传播媒体之一，因此有必要研究信息在社交网络上的传播规律. 本文探索了包含遏制机制和遗忘机制的信息传播机理，提出了信息传播的模型，给出了信息传播的规则，建立了相应的平均场方程，计算了平衡点和基本再生数R0，并从理论上证明了平衡点的渐进稳定性. 仿真实验分析了遏制机制、遗忘机制等因素对信息传播过程的影响，并验证了所得结论的正确性.

关键词:

Social networks have been developed into one of the most important media for information propagation, and it is necessary to disclose how the information disseminates over social networks. In this paper, we explore the spreading mechanism including information stifling and forgetting, establish a spreading model, and elaborate the spreading rules. According to the spreading model, we build the mean field equation, calculate the two equilibriums and the basic reproduction number R0, and prove theoretically the asymptotical stability of the equilibriums. We analyze the effects of stifling mechanism and forgetting mechanism on the information spreading process, and validate the results of theoretical analysis by numerical simulations.

Keywords:

作者及机构信息

1.
西安电子科技大学计算机学院, 西安 710071;

2.
陕西省网络与系统安全重点实验室, 西安 710071

基金项目: 长江学者和创新团队发展计划项目（批准号：IRT1078）、国家自然基金委员会-广东联合基金重点基金（批准号：U1135002）、国家科技部重大专项（批准号：2011ZX03005-002）、国家自然科学基金（批准号：61173135）和中央高校基本科研业务费（批准号：JY10000903001，K5051303007，K5051203012）资助的课题.

Authors and contacts

1.
School of Computer Science and technology, Xidian University, Xi'an 710071, China;

2.
Shaanxi Key Laboratory of Network and System Security, Xidian University, Xi'an 710071, China

Funds: Project supported by the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRT1078), the Key Program of NSFC-Guangdong Union Foundation (Grant No. U1135002), the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2011ZX03005-002), the National Natural Science Foundation of China (Grant No. 61173135), and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant Nos. JY10000903001, K5051303007, K5051203012).

参考文献

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[6]	May R M, Lloyd A L 2001 Phys. Rev. E 64 066112
[7]	Moreno Y, Pastor Satorras R, Vespignani A 2002 Europ. Phys. J. B 26 521
[8]	Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189
[9]	Wang J, Zhao L, Huang R 2014 Physica A: Statistical Mechanics and its Applications 398 43
[10]	Isham V, Harden S, Nekovee M 2010 Physica A 389 561
[11]	Zhao L, Wang Q, Cheng J, Chen Y, Wang J, Huang W 2011 Physica A: Statistical Mechanics and its Applications 390 2619
[12]	Zhao L, Xie W, Gao H O, Qiu X, Wang X, Zhang S 2013 Physica A: Statistical Mechanics and its Applications 392 6146
[13]	Zhao L, Wang J, Chen Y, Wang Q, Cheng J, Cui H 2012 Physica A: Statistical Mechanics and its Applications 391 2444
[14]	Gong Y W, Song Y R, Jiang G P 2012 Chin. Phys. B 21 010205
[15]	Lu Y L, Jiang G P, Song Y R 2012 Chin. Phys. B 21 100207
[16]	Pastor Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[17]	Zhu G, Fu X, Chen G 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 2588
[18]	Yang M, Chen G, Fu X 2011 Physica A: Statistical Mechanics and its Applications 390 2408
[19]	Lu Y L, Jiang G P, Song Y R 2013 Acta Phys. Sin. 62 130202(in Chinese)[鲁延玲, 蒋国平, 宋玉蓉 2013 62 130202]
[20]	Zhang J, Sun J 2014 Physica A: Statistical Mechanics and its Applications 394 24
[21]	d'Onofrio A 2008 Nonlinear Analysis: Real World Applications 9 1567
[22]	Wang Y, Jin Z, Yang Z, Zhang Z K, Zhou T, Sun G Q 2012 Nonlinear Analysis: Real World Application 13 543
[23]	Wang J, Liu M, Li Y 2013 Physica A: Statistical Mechanics and its Applications 392 1621
[24]	Wang Y, Cao J, Jin Z, Zhang H, Sun G Q 2013 Physica A: Statistical Mechanics and its Applications 392 5824
[25]	Zhou Y, Xia Y 2014 Physica A: Statistical Mechanics and its Applications 399 16
[26]	Feng Y, Fan Q, Ma L, Ding L 2014 Physica A: Statistical Mechanics and its Applications 393 277
[27]	Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[28]	Li C H, Tsai C C, Yang S Y 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 1042
[29]	Liu J, Zhang T 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3375
[30]	Gong Y W, Song Y R, Jiang G P 2012 Acta Phys. Sin. 61 110205(in Chinese)[巩永旺, 宋玉蓉, 蒋国平 2012 61 110205]
[31]	Zhu G, Fu X, Chen G 2012 Appl. Math. Model. 36 5808
[32]	Gu J, Li W, Cai X 2008 Europ. Phys. J. B 62 247
[33]	Ebbinghaus H 2010 Memory: A Contribution to Experimental Psychology (Whitefish: Nabu Press) pp18-22
[34]	van den Driessche P, Watmough J 2002 Math. Biosci. 180 29

施引文献

[1]	Guan W, Gao H, Yang M, Li Y, Ma H, Qian W, Cao Z, Yang X 2014 Physica A: Statistical Mechanics and its Applications 395 340
[2]	Zhang Y C, Liu Y, Zhang H F, Cheng H, Xiong F 2011 Acta Phys. Sin. 60 050501(in Chinese)[张彦超, 刘云, 张海峰, 程辉, 熊菲 2011 60 050501]
[3]	Zhao L, Guan X H, Yuan R X 2012 Knowledge and Information Systems 31 371
[4]	Leskovec J, McGlohon M, Faloutsos C, Glance N, Hurst M 2007 International Conference on Data Mining, Proceedings of the 7th SIAM International Conference on Data Mining Minneapolis, Minnesota, USA, April 26-28, 2007 p551
[5]	Xu R Z, Li H L, Xing C M 2013 Int. J. Comput. Sci. Appl. 1 1
[6]	May R M, Lloyd A L 2001 Phys. Rev. E 64 066112
[7]	Moreno Y, Pastor Satorras R, Vespignani A 2002 Europ. Phys. J. B 26 521
[8]	Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189
[9]	Wang J, Zhao L, Huang R 2014 Physica A: Statistical Mechanics and its Applications 398 43
[10]	Isham V, Harden S, Nekovee M 2010 Physica A 389 561
[11]	Zhao L, Wang Q, Cheng J, Chen Y, Wang J, Huang W 2011 Physica A: Statistical Mechanics and its Applications 390 2619
[12]	Zhao L, Xie W, Gao H O, Qiu X, Wang X, Zhang S 2013 Physica A: Statistical Mechanics and its Applications 392 6146
[13]	Zhao L, Wang J, Chen Y, Wang Q, Cheng J, Cui H 2012 Physica A: Statistical Mechanics and its Applications 391 2444
[14]	Gong Y W, Song Y R, Jiang G P 2012 Chin. Phys. B 21 010205
[15]	Lu Y L, Jiang G P, Song Y R 2012 Chin. Phys. B 21 100207
[16]	Pastor Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[17]	Zhu G, Fu X, Chen G 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 2588
[18]	Yang M, Chen G, Fu X 2011 Physica A: Statistical Mechanics and its Applications 390 2408
[19]	Lu Y L, Jiang G P, Song Y R 2013 Acta Phys. Sin. 62 130202(in Chinese)[鲁延玲, 蒋国平, 宋玉蓉 2013 62 130202]
[20]	Zhang J, Sun J 2014 Physica A: Statistical Mechanics and its Applications 394 24
[21]	d'Onofrio A 2008 Nonlinear Analysis: Real World Applications 9 1567
[22]	Wang Y, Jin Z, Yang Z, Zhang Z K, Zhou T, Sun G Q 2012 Nonlinear Analysis: Real World Application 13 543
[23]	Wang J, Liu M, Li Y 2013 Physica A: Statistical Mechanics and its Applications 392 1621
[24]	Wang Y, Cao J, Jin Z, Zhang H, Sun G Q 2013 Physica A: Statistical Mechanics and its Applications 392 5824
[25]	Zhou Y, Xia Y 2014 Physica A: Statistical Mechanics and its Applications 399 16
[26]	Feng Y, Fan Q, Ma L, Ding L 2014 Physica A: Statistical Mechanics and its Applications 393 277
[27]	Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[28]	Li C H, Tsai C C, Yang S Y 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 1042
[29]	Liu J, Zhang T 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 3375
[30]	Gong Y W, Song Y R, Jiang G P 2012 Acta Phys. Sin. 61 110205(in Chinese)[巩永旺, 宋玉蓉, 蒋国平 2012 61 110205]
[31]	Zhu G, Fu X, Chen G 2012 Appl. Math. Model. 36 5808
[32]	Gu J, Li W, Cai X 2008 Europ. Phys. J. B 62 247
[33]	Ebbinghaus H 2010 Memory: A Contribution to Experimental Psychology (Whitefish: Nabu Press) pp18-22
[34]	van den Driessche P, Watmough J 2002 Math. Biosci. 180 29

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