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According to directed Email networks and the spread characteristics of Email virus, we study the behavior of the virus shock propagation in Email networks by using the mean field method to build delay differential equation model of viral spread. Then, the sufficient condition about the existence of shock solution's global attractor is given in theory. The existence and control of attractor are proved by numerical experiments. Our research indicates that spread probability between subgraphs determines the existence of attractor, and effective rate of spread determines the amplitude of attractor. Therefore these two parameters are significant in prediction of the scale of viral spread in networks.
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Keywords:
- complex network /
- Email virus /
- spread /
- global attractor
[1] Newman M, Watts D J 1999 Phys. Rev. E 60 7332
[2] Zou C C, Towsley D, Gong W B 2007 IEEE 4 105
[3] Pastor S R, Vespignani A 2001 Phys. Rev. E 63 066117
[4] Watts D J, Strogatz S H 1988 Nature 393 (6684) 440
[5] Ustin B 2004 Science 304 (5670) 527
[6] Driver R D1977 Ordinary and Delay Differential Equations (New York: Springer-Verlag) p28
[7] Feedman H I 1980 Deterministic Mathematical Models in population Ecology (New York: Marcel Dekker) p60
[8] Hale J k 2003 Theory of functional Differential Equations (New York: Springer-Verlag) p101
[9] Li X, Wang X F 2007 Science 38 (5) 401
[10] Xu D, Li X, Wang X F 2007 Acta Phys. Sin. 56 1313 (in Chinese) [徐丹, 李翔, 汪小帆 2007 56 1313]
[11] Weng W G, Ni S J, Shen S F, Yuan H Y 2007 Acta Phys. Sin. 56 1938 (in Chinese) [翁文国, 倪顺江, 申世飞, 袁宏永 2007 56 1938]
[12] Newman M E J, Forrest S, Balthrop J 2002 Phys. Rev. E 66 035101
[13] Kari J 2005 Theoretical Computer Science 334 3
[14] Lee D D, Seung H S 1999 Nature 401 788
[15] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[16] Guo D J, Lakshmikantham V 1988 Nonlinear Problems in Abstract Cones (New York: Academic Press) p86
[17] Guo D 1986 Nonlinear Anal. TMA. 10 1293
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[1] Newman M, Watts D J 1999 Phys. Rev. E 60 7332
[2] Zou C C, Towsley D, Gong W B 2007 IEEE 4 105
[3] Pastor S R, Vespignani A 2001 Phys. Rev. E 63 066117
[4] Watts D J, Strogatz S H 1988 Nature 393 (6684) 440
[5] Ustin B 2004 Science 304 (5670) 527
[6] Driver R D1977 Ordinary and Delay Differential Equations (New York: Springer-Verlag) p28
[7] Feedman H I 1980 Deterministic Mathematical Models in population Ecology (New York: Marcel Dekker) p60
[8] Hale J k 2003 Theory of functional Differential Equations (New York: Springer-Verlag) p101
[9] Li X, Wang X F 2007 Science 38 (5) 401
[10] Xu D, Li X, Wang X F 2007 Acta Phys. Sin. 56 1313 (in Chinese) [徐丹, 李翔, 汪小帆 2007 56 1313]
[11] Weng W G, Ni S J, Shen S F, Yuan H Y 2007 Acta Phys. Sin. 56 1938 (in Chinese) [翁文国, 倪顺江, 申世飞, 袁宏永 2007 56 1938]
[12] Newman M E J, Forrest S, Balthrop J 2002 Phys. Rev. E 66 035101
[13] Kari J 2005 Theoretical Computer Science 334 3
[14] Lee D D, Seung H S 1999 Nature 401 788
[15] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[16] Guo D J, Lakshmikantham V 1988 Nonlinear Problems in Abstract Cones (New York: Academic Press) p86
[17] Guo D 1986 Nonlinear Anal. TMA. 10 1293
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