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Based on the lattice hydrodynamic model with bidirectional pedestrian flow, the lattice hydrodynamic model which considered the interaction of the next-nearest-neighbor pedestrians was proposed in this paper. By the linear stability analysis, the stability condition was obtained. By nonlinear analysis, the modified Korteweg-de Vries equation to describe the density wave of pedestrian congestion was given. Furthermore, numerical simulation was carried out to examine the performance of such a model and it shows consistency with the theoretical analysis results.
[1] ［1］Chowdhury D, Santen L, Schadschneider A 2000 Phys. Rep. 329 199
[2] ［2］Helbing D 2001 Rev. Mod. Phys. 73 1067
[3] ［3］Nagatani T 2002 Rep. Prog. Phys. 65 1331
[4] ［4］Helbing D, Farkas I J, Vicsek T 2000 Phys. Rev. Lett. 84 1240
[5] ［5］Helbing D, Farkas I J, Vicsek T 2000 Nature 407 487
[6] ［6］Bohannon J 2005 Science 310 219
[7] ［7］Henderson L E 1971 Nature 229 381
[8] ［8］Helbing D, Molna′r P 1995 Phys. Rev. E 51 4282
[9] ［9］Muramatsu M, Irie T, Nagatani T 1999 Physica A 267 487
[10] ］Tajima Y, Nagatani T 2001 Physica A 292 545
[11] ］Tajima Y, Nagatani T 2002 Physica A 303 239
[12] ］Takimoto K, Tajima Y, Nagatani T 2002 Physica A 308 460
[13] ］Burstedde C, Klauck K, Schadschneider A, Zittarz J 2001 Physica A 295 507
[14] ］ Yue H, Shao C F, Yao Z S 2009 Acta Phys. Sin. 58 4523 (in Chinese)［岳昊、 邵春福、 姚智胜 2009 58 4523］
[15] ］Zhou J W, Kuan H, Liu M R, Kong L J 2009 Acta Phys. Sin. 58 3001 (in Chinese)［周金旺、 邝华、 刘慕仁、 孔令江 2009 58 3001］
[16] ］Kerner B S, Konhauser P 1993 Phys. Rev. E 48 2335
[17] ］Kurtze D A, Hong D C 1995 Phys. Rev. E 52 218
[18] ］Komatsu T S, Sasa S 1995 Phys. Rev. E 52 5574
[19] ］Muramatsu M, Nagatani T 1999 Phys. Rev. E 60 180
[20] ］Nagatani T 1998 Physica A 261 599
[21] ］Nagatani T 1999 Physica A 264 581
[22] ］Nagatani T 1999 Physica A 265 297
[23] ］Nagatani T 1999 Phys. Rev. E 59 4857
[24] ］Xue Y 2004 Acta Phys. Sin. 53 25 (in Chinese)［薛郁 2004 53 25］
[25] ］Tang T Q, Huang H J， Xue Y 2006 Acta Phys. Sin. 55 4026 (in Chinese)［唐铁桥、 黄海军、 薛郁 2006 55 4026］
[26] ］May A D 1990 Traffic Flow Fundamentals (New Jersey： Prentice Hall) p210
[27] ］Tian H H， Xue Y， He H D， Wei Y F， Lu W Z 2009 Physica A 388 2895
[28] ］Xue Y, Tian H H, He H D, Lu W Z, Wei Y F 2009 Eur. Phys. J. B 69 289
[29] ］Nagatani T, Nakanishi K 1998 Phys. Rev. E 57 6415
[30] ］Nagatani T 1998 Phys. Rev. E 58 4271
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[1] ［1］Chowdhury D, Santen L, Schadschneider A 2000 Phys. Rep. 329 199
[2] ［2］Helbing D 2001 Rev. Mod. Phys. 73 1067
[3] ［3］Nagatani T 2002 Rep. Prog. Phys. 65 1331
[4] ［4］Helbing D, Farkas I J, Vicsek T 2000 Phys. Rev. Lett. 84 1240
[5] ［5］Helbing D, Farkas I J, Vicsek T 2000 Nature 407 487
[6] ［6］Bohannon J 2005 Science 310 219
[7] ［7］Henderson L E 1971 Nature 229 381
[8] ［8］Helbing D, Molna′r P 1995 Phys. Rev. E 51 4282
[9] ［9］Muramatsu M, Irie T, Nagatani T 1999 Physica A 267 487
[10] ］Tajima Y, Nagatani T 2001 Physica A 292 545
[11] ］Tajima Y, Nagatani T 2002 Physica A 303 239
[12] ］Takimoto K, Tajima Y, Nagatani T 2002 Physica A 308 460
[13] ］Burstedde C, Klauck K, Schadschneider A, Zittarz J 2001 Physica A 295 507
[14] ］ Yue H, Shao C F, Yao Z S 2009 Acta Phys. Sin. 58 4523 (in Chinese)［岳昊、 邵春福、 姚智胜 2009 58 4523］
[15] ］Zhou J W, Kuan H, Liu M R, Kong L J 2009 Acta Phys. Sin. 58 3001 (in Chinese)［周金旺、 邝华、 刘慕仁、 孔令江 2009 58 3001］
[16] ］Kerner B S, Konhauser P 1993 Phys. Rev. E 48 2335
[17] ］Kurtze D A, Hong D C 1995 Phys. Rev. E 52 218
[18] ］Komatsu T S, Sasa S 1995 Phys. Rev. E 52 5574
[19] ］Muramatsu M, Nagatani T 1999 Phys. Rev. E 60 180
[20] ］Nagatani T 1998 Physica A 261 599
[21] ］Nagatani T 1999 Physica A 264 581
[22] ］Nagatani T 1999 Physica A 265 297
[23] ］Nagatani T 1999 Phys. Rev. E 59 4857
[24] ］Xue Y 2004 Acta Phys. Sin. 53 25 (in Chinese)［薛郁 2004 53 25］
[25] ］Tang T Q, Huang H J， Xue Y 2006 Acta Phys. Sin. 55 4026 (in Chinese)［唐铁桥、 黄海军、 薛郁 2006 55 4026］
[26] ］May A D 1990 Traffic Flow Fundamentals (New Jersey： Prentice Hall) p210
[27] ］Tian H H， Xue Y， He H D， Wei Y F， Lu W Z 2009 Physica A 388 2895
[28] ］Xue Y, Tian H H, He H D, Lu W Z, Wei Y F 2009 Eur. Phys. J. B 69 289
[29] ］Nagatani T, Nakanishi K 1998 Phys. Rev. E 57 6415
[30] ］Nagatani T 1998 Phys. Rev. E 58 4271
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