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研究了一类周期变化的非线性复杂发病率的广义流行病学模型(SIR(susceptible, infected, recovered)模型). 通过一系列坐标变换将原模型转化为Hamilton系统,运用Melnikov方法证明了该系统存在混沌运动,给出了发生同宿分岔的条件,并用数值模拟验证了上述结果.
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关键词:
- SIR(susceptible /
- infected /
- recovered)模型 /
- 混沌运动 /
- Melnikov方法 /
- 同宿分岔
[1] Kermack W O, McKendrick A G 1927 Proc. Roy. Soc. A 115 700
[2] Anderson R M, May R M 1991 Infectious Diseases of Humans (Oxford: Oxford University Press)
[3] Aron J L, Schwartz I B 1984 Theor. Biol. 110 665
[4] Kuznetsov, Yu A, Piccardi C 1994 Math. Biol. 32 109
[5] Olsen L F, Shaffer W M 1990 Science 249 499
[6] Hethcote H W, Driessche P V D 1991 Math. Biol. 29 271
[7] Liu W M, Hethcote H W, Levin S A 1987 Math. Biol. 25 359
[8] Liu W M, Levin S A, Iwasa Y 1986 Math. Biol. 23 187
[9] Yi H T 2009 MS dissertation (Hunan: Hunan university) (in Chinese) [尹海涛 2009 硕士学位论文(湖南:湖南大学)]
[10] Li J 2005 MS dissertation (Nanjing: Nanjing university of science and technology) (in Chinese) [李 静 2005 硕士学位论文 (南京:南京理工大学)] 〖11] Ni S J, Weng W G, Fan W C 2009 Acta Phys. Sin. 58 3707 (in Chinese) [倪顺江、翁文国、范维澄 2009 物理学报 58 3707]
[11] Liu M X, Ruan J 2009 Chin. Phys. B 18 2115
[12] Liu M X, Ruan J 2009 Chin. Phys. B 18 5111
[13] Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[14] Pei W D, Chen Z Q, Yuan Z Z 2008 Chin. Phys. B 17 0373
[15] Zhong L, Weng J Q 2000 Acta Phys. Sin. 49 0626 (in Chinese) [钟 玲、翁甲强 2000 物理学报 49 0626]
[16] Xu D, Li X, Wang X F 2007 Acta Phys. Sin. 56 1313 (in Chinese) [许 丹、李 翔、汪小帆 2007 物理学报 56 1313]
[17] Glendinning P, Perry L P 1997 Math. Biol. 34 359
[18] Chow S N, Li C Z, Wang D 1994 Normal forms and bifurcation of plannar vector fields (Cambridge: Cambridge University Press)
[19] Yang X L, Xu W, Sun Z K 2006 Acta Phys. Sin. 55 1678 (in Chinese) [杨晓丽、徐 伟、孙中奎 2006 物理学报 55 1678]
[20] Liu Z R 2002 The analytical method of chaos (Shanghai:Shanghai university press) p56 (in Chinese) [刘增荣 2002 混沌研究中的解析方法(上海:上海大学出版社)第56页]
[21] Lei Y M, Xu W 2007 Acta Phys. Sin. 56 5103 (in Chinese) [雷佑銘、徐 伟 2007 物理学报 56 5103]
[22] Guckenheimer J, Holmes P 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vectors Fields (New York: New York Springer)
[23] Yang X L, Xu W 2009 Acta Phys Sin. 58 3722 (in Chinese) [杨晓丽、徐 伟 2009 物理学报 58 3722]
[24] Baesens N C, Nicolis G 1983 Z. Phys. B 52 345
-
[1] Kermack W O, McKendrick A G 1927 Proc. Roy. Soc. A 115 700
[2] Anderson R M, May R M 1991 Infectious Diseases of Humans (Oxford: Oxford University Press)
[3] Aron J L, Schwartz I B 1984 Theor. Biol. 110 665
[4] Kuznetsov, Yu A, Piccardi C 1994 Math. Biol. 32 109
[5] Olsen L F, Shaffer W M 1990 Science 249 499
[6] Hethcote H W, Driessche P V D 1991 Math. Biol. 29 271
[7] Liu W M, Hethcote H W, Levin S A 1987 Math. Biol. 25 359
[8] Liu W M, Levin S A, Iwasa Y 1986 Math. Biol. 23 187
[9] Yi H T 2009 MS dissertation (Hunan: Hunan university) (in Chinese) [尹海涛 2009 硕士学位论文(湖南:湖南大学)]
[10] Li J 2005 MS dissertation (Nanjing: Nanjing university of science and technology) (in Chinese) [李 静 2005 硕士学位论文 (南京:南京理工大学)] 〖11] Ni S J, Weng W G, Fan W C 2009 Acta Phys. Sin. 58 3707 (in Chinese) [倪顺江、翁文国、范维澄 2009 物理学报 58 3707]
[11] Liu M X, Ruan J 2009 Chin. Phys. B 18 2115
[12] Liu M X, Ruan J 2009 Chin. Phys. B 18 5111
[13] Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[14] Pei W D, Chen Z Q, Yuan Z Z 2008 Chin. Phys. B 17 0373
[15] Zhong L, Weng J Q 2000 Acta Phys. Sin. 49 0626 (in Chinese) [钟 玲、翁甲强 2000 物理学报 49 0626]
[16] Xu D, Li X, Wang X F 2007 Acta Phys. Sin. 56 1313 (in Chinese) [许 丹、李 翔、汪小帆 2007 物理学报 56 1313]
[17] Glendinning P, Perry L P 1997 Math. Biol. 34 359
[18] Chow S N, Li C Z, Wang D 1994 Normal forms and bifurcation of plannar vector fields (Cambridge: Cambridge University Press)
[19] Yang X L, Xu W, Sun Z K 2006 Acta Phys. Sin. 55 1678 (in Chinese) [杨晓丽、徐 伟、孙中奎 2006 物理学报 55 1678]
[20] Liu Z R 2002 The analytical method of chaos (Shanghai:Shanghai university press) p56 (in Chinese) [刘增荣 2002 混沌研究中的解析方法(上海:上海大学出版社)第56页]
[21] Lei Y M, Xu W 2007 Acta Phys. Sin. 56 5103 (in Chinese) [雷佑銘、徐 伟 2007 物理学报 56 5103]
[22] Guckenheimer J, Holmes P 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vectors Fields (New York: New York Springer)
[23] Yang X L, Xu W 2009 Acta Phys Sin. 58 3722 (in Chinese) [杨晓丽、徐 伟 2009 物理学报 58 3722]
[24] Baesens N C, Nicolis G 1983 Z. Phys. B 52 345
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