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Human behaviors are usually determined by some social and/or economic trend. In the past few years, many attempts have been made, in the field of complex scientific systems, to describe the dynamics of these behaviors quantitatively and have an accurate understanding of the corresponding mechanisms. In this paper, a generalized potential, that is, a migration desire function defined by the age of the migrating people, the migrating distance, and the so-called economic-population density of the emigration area, is proposed. It can be transformed into Hamilton-Jacobi equation by using a random dynamical method, Langevin equation, so that the decision-making behavior can be investigated, based on a statistic framework during a group migration process. By taking use of the multi-dimensional steepest descent method, the Hamilton-Jacobi equation is solved; the solution shows that the information entropy of the system varies, leading by a single peak, as the age of the migrating people increases. It also demonstrates that the second derivative of the migrating distance to the information entropy has a change of zero-crossing (which actually means a phase change). The third characteristic of the solution is that the information entropy follows another single peak as the economic-population density increases. A deeper analysis reveals the significance behind these findings and the corresponding mechanisms. So some new understandings of the group human behaviors can be obtained, and some worthy references can be provided for some related administrative offices.
[1] Barabasi A L 2005 Nature 435 207
[2] Li N N, Zhou T, Zhang N 2008 Complex System and Complexity Science 5(2) 15 (in Chinese) [李楠楠, 周涛, 张宁 2008 复杂系统与复杂性科学 5(2) 15]
[3] Fan C, Guo J L, Han X P, Wang B H 2011 Complex System and Complexity Science 8(2) 1 (in Chines) [樊超, 郭进利, 韩筱璞, 汪秉宏2011 复杂系统与复杂性科学, 8(2) 1]
[4] Boyd R, Richerson P J 2009 J. Theor. Biol. 257 331
[5] Reynolds C 1987 Comput. Graph. 21 25
[6] Vicsek T, Czirók A, Ben-Jacob E, Cohen I, Shochet O 1995 Phys. Rev. Lett. 75 1226
[7] Helbing D, Farkas I, Vicsek T 2000 Nature 407 487
[8] Sung M, Gleicher M, Chenney S 2004 Eurographics 23 519
[9] Nie L R, Mei D C 2007 EPL 79 20005
[10] Corradini O, Faccioli P, Orland H 2009 Phys. Rev. E 80 061112
[11] Faccioli P, Sega M, Pederiva F, Orland H 2006 Phys. Rev. Lett. 97 108101
[12] Chai L H 2004 Int. J. Therm. Sci. 43 1067
[13] Haken H 1983 Advanced Synergetics (Berlin: Springer-Verlag) 42
[14] Gong K, Tang M, Shang M S, Zhou T 2012 Acta Phys. Sin. 61 098901 (in Chinese) [龚凯, 唐明, 尚明生, 周涛 2012 物理学报 61 098901]
[15] González M C, Hidalgo C A, Barabási A L 2008 Nature 453 779
[16] Brockmann D D, Hufnagel L, Geisel T 2006 Nature 439 462
[17] Sega M, Faccioli P, Pederiva F, Garberoglio G, Orland H 2007 Phys. Rev. Lett. 99 118102
[18] 18Ovidiu C 2009 Asymptotics and Borel summability (Boca Raton: Chapman & Hall/CRC Press) pp33-88
[19] Lin Z Q, Ye G X 2013 Chin. Phys. B 22 058201
[20] Xu X L, Fu C H, Liu C P, He D R 2010 Chin. Phys. B 19 060501R
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[1] Barabasi A L 2005 Nature 435 207
[2] Li N N, Zhou T, Zhang N 2008 Complex System and Complexity Science 5(2) 15 (in Chinese) [李楠楠, 周涛, 张宁 2008 复杂系统与复杂性科学 5(2) 15]
[3] Fan C, Guo J L, Han X P, Wang B H 2011 Complex System and Complexity Science 8(2) 1 (in Chines) [樊超, 郭进利, 韩筱璞, 汪秉宏2011 复杂系统与复杂性科学, 8(2) 1]
[4] Boyd R, Richerson P J 2009 J. Theor. Biol. 257 331
[5] Reynolds C 1987 Comput. Graph. 21 25
[6] Vicsek T, Czirók A, Ben-Jacob E, Cohen I, Shochet O 1995 Phys. Rev. Lett. 75 1226
[7] Helbing D, Farkas I, Vicsek T 2000 Nature 407 487
[8] Sung M, Gleicher M, Chenney S 2004 Eurographics 23 519
[9] Nie L R, Mei D C 2007 EPL 79 20005
[10] Corradini O, Faccioli P, Orland H 2009 Phys. Rev. E 80 061112
[11] Faccioli P, Sega M, Pederiva F, Orland H 2006 Phys. Rev. Lett. 97 108101
[12] Chai L H 2004 Int. J. Therm. Sci. 43 1067
[13] Haken H 1983 Advanced Synergetics (Berlin: Springer-Verlag) 42
[14] Gong K, Tang M, Shang M S, Zhou T 2012 Acta Phys. Sin. 61 098901 (in Chinese) [龚凯, 唐明, 尚明生, 周涛 2012 物理学报 61 098901]
[15] González M C, Hidalgo C A, Barabási A L 2008 Nature 453 779
[16] Brockmann D D, Hufnagel L, Geisel T 2006 Nature 439 462
[17] Sega M, Faccioli P, Pederiva F, Garberoglio G, Orland H 2007 Phys. Rev. Lett. 99 118102
[18] 18Ovidiu C 2009 Asymptotics and Borel summability (Boca Raton: Chapman & Hall/CRC Press) pp33-88
[19] Lin Z Q, Ye G X 2013 Chin. Phys. B 22 058201
[20] Xu X L, Fu C H, Liu C P, He D R 2010 Chin. Phys. B 19 060501R
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