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Bootstrap percolation was first used in statistic physics to study the phenomenon that magnetic-order goes down and disappears because of the disturbance of nonmagnetic impurity. With the development of complex network, the application of bootstrap percolation in network has attracted much attention. In the real world, many systems naturally exhibit the two-branch structure. And bipartite network is one of important networks in complex networks. In this paper, we use the dynamics equation and computational simulation to study the bootstrap percolation in bipartite networks. The parameters we focus on are the node initial active ratios f1 and f2 and active thresholds Ω1, and Ω2. We draw the conclusion that the ratio of active nodes has discontinuous transition, which will gradually disappear with parameters varying. We also prove the consistency between the dynamic equation and simulation results.
[1] Chalupa J, Leath P L, Reich G R 1979 J. Phys. C 12 L31
[2] Wu K, Gu Z N 1996 Acta Phys. Sin. 45 1905 (in Chinese) [吴克,顾镇南 1996 45 1905]
[3] Yi L, Xiao Y, Yao K L 1993 Acta Phys. Sin. (Overseas Ed.) 2 458
[4] Zheng M S, Liu Y P 1993 Acta Phys. Sin. 42 304 (in Chinese) [郑茂盛,刘云鹏 1993 42 304]
[5] Ye G X, Xu Y Q, Wang J S, Zhang Q R 1994 Acta Phys. Sin. 43 4 (in Chinese) [叶高翔,许宇庆,王劲松,张其瑞 1994 43 4]
[6] Eckmann J P, Feinerman O, Gruendlinger L, Moses E, Soriano J, Tlusty T 2007 Phys. Rep. 449 54
[7] Soriano J, Marttnez M R, Tlusty T, Moses E 2008 Proc. Natl. Acad. Sci. 105 13758
[8] Goltsev A V, Abreu F V de, Dorogovtsev S N, Mendes J F F 2010 Phys. Rev. E 81 1921
[9] Adler J, Palmer R G, Meyer H M 1987 Phys. Rev. Lett. 58 882
[10] Nakanishi H, Takano H 1986 Phys. Lett. ll5A 117
[11] Ertel W, Frobose K, Jackle J 1988 J. Chem. Phys. 88 5027
[12] Sellitto M, Biroli G, Toninell C 2005 Europhys. Lett. 69 496
[13] Toninelli C, Biroli G, Fisher D S 2006 Phys. Rev. Lett. 96 5702
[14] Chalupa J, Leath P L, Reich G R 1981 J. Phys. C: Solid State Phys. 14 3187
[15] Ma Z F, Zhang P, Wu Y, Li W H, Zhuang Y Q, Du L 2010 Chin. Phys. B 19 7201
[16] Holroyd A E 2003 Probab. Theory Relat. Fields 125 195
[17] Holroyd A E 2006 Electron. J. Probab. 11 418
[18] Balogh J, Bollobas B 2006 Probab. Theory Relat. Fields 134 624
[19] Balogh J, Pittel B G 2007 Random Struct. Alg. 30 257
[20] Fontes L R G, Schonmann R H 2008 J. Stat. Phys. 132 839
[21] Watts D J 2002 PNAS 99 5766
[22] Baxter G J, Dorogovtsev S N, Goltsev A V Mendes J F F 2010 Phys. Rev. E 82 1103
[23] Chen H B, Fan Y, Fang J Q, Di Z R 2007 Acta Phys. Sin. 58 1383 (in Chinese) [陈宏斌,樊瑛,方锦清,狄增如 2007 58 1383]
[24] Fan Y, Suo L N, Shen X S, Hu Y Q 2008 J. BNU (Natural Science) 44 103 (in Chinese) [樊瑛, 索丽娜, 沈晓松, 胡延庆 2008 北京师范大学学报 (自然科学版) 44 103]
[25] Ma W D, Wang L, Li R P, Shui H S, Zhou M T 2008 Acta Phys. Sin. 57 1381 (in Chinese) [马卫东,王磊,李幼平,水鸿寿,周明天 2008 57 1381]
[26] Latapy M, Magnien C, Vecchio N D 2008 Soc. Networks 30 31
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[1] Chalupa J, Leath P L, Reich G R 1979 J. Phys. C 12 L31
[2] Wu K, Gu Z N 1996 Acta Phys. Sin. 45 1905 (in Chinese) [吴克,顾镇南 1996 45 1905]
[3] Yi L, Xiao Y, Yao K L 1993 Acta Phys. Sin. (Overseas Ed.) 2 458
[4] Zheng M S, Liu Y P 1993 Acta Phys. Sin. 42 304 (in Chinese) [郑茂盛,刘云鹏 1993 42 304]
[5] Ye G X, Xu Y Q, Wang J S, Zhang Q R 1994 Acta Phys. Sin. 43 4 (in Chinese) [叶高翔,许宇庆,王劲松,张其瑞 1994 43 4]
[6] Eckmann J P, Feinerman O, Gruendlinger L, Moses E, Soriano J, Tlusty T 2007 Phys. Rep. 449 54
[7] Soriano J, Marttnez M R, Tlusty T, Moses E 2008 Proc. Natl. Acad. Sci. 105 13758
[8] Goltsev A V, Abreu F V de, Dorogovtsev S N, Mendes J F F 2010 Phys. Rev. E 81 1921
[9] Adler J, Palmer R G, Meyer H M 1987 Phys. Rev. Lett. 58 882
[10] Nakanishi H, Takano H 1986 Phys. Lett. ll5A 117
[11] Ertel W, Frobose K, Jackle J 1988 J. Chem. Phys. 88 5027
[12] Sellitto M, Biroli G, Toninell C 2005 Europhys. Lett. 69 496
[13] Toninelli C, Biroli G, Fisher D S 2006 Phys. Rev. Lett. 96 5702
[14] Chalupa J, Leath P L, Reich G R 1981 J. Phys. C: Solid State Phys. 14 3187
[15] Ma Z F, Zhang P, Wu Y, Li W H, Zhuang Y Q, Du L 2010 Chin. Phys. B 19 7201
[16] Holroyd A E 2003 Probab. Theory Relat. Fields 125 195
[17] Holroyd A E 2006 Electron. J. Probab. 11 418
[18] Balogh J, Bollobas B 2006 Probab. Theory Relat. Fields 134 624
[19] Balogh J, Pittel B G 2007 Random Struct. Alg. 30 257
[20] Fontes L R G, Schonmann R H 2008 J. Stat. Phys. 132 839
[21] Watts D J 2002 PNAS 99 5766
[22] Baxter G J, Dorogovtsev S N, Goltsev A V Mendes J F F 2010 Phys. Rev. E 82 1103
[23] Chen H B, Fan Y, Fang J Q, Di Z R 2007 Acta Phys. Sin. 58 1383 (in Chinese) [陈宏斌,樊瑛,方锦清,狄增如 2007 58 1383]
[24] Fan Y, Suo L N, Shen X S, Hu Y Q 2008 J. BNU (Natural Science) 44 103 (in Chinese) [樊瑛, 索丽娜, 沈晓松, 胡延庆 2008 北京师范大学学报 (自然科学版) 44 103]
[25] Ma W D, Wang L, Li R P, Shui H S, Zhou M T 2008 Acta Phys. Sin. 57 1381 (in Chinese) [马卫东,王磊,李幼平,水鸿寿,周明天 2008 57 1381]
[26] Latapy M, Magnien C, Vecchio N D 2008 Soc. Networks 30 31
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