徐瑞，山西大学复杂系统研究所教授、博士生导师

电子邮箱：xurui@sxu.edu.cn

通信地址：山西省太原市坞城路92号山西大学复杂系统研究所

教育经历

2002年3月-2005年2月，The University of Dundee，博士，导师： Professors Mark Chaplain and Fordyce Davidson

工作经历

2018年8月-至今，山西大学复杂系统研究所，教授，博士生导师

2006年10月-2009年9月，西安交通大学数学博士后，合作导师：马知恩教授

科研项目

1. 基于游离病毒和细胞-细胞传播的HIV免疫-流行病学嵌套动力学的建模与研

究，国家自然科学基金面上项目（项目负责人；项目编号：11871316；2019年1月-2022年12月）。

2. 具有类年龄结构和空间异质性的传染病动力学的建模与研究，国家自然科学

基金面上项目（项目负责人；项目编号：11371368；2014年1月-2017年12月）。

3. 具有空间效应的传染病动力学模型的建立与研究，国家自然科学基金面上项

目（项目负责人；项目编号：11071254；2011年1月-2013年12月）。

4. 具有时空滞后的反应扩散种群模型的建立与研究，国家自然科学基金面上项

目（项目负责人；项目编号：10671209；2007年1月-2009年12月)。

5. 集合种群尺度下种群动力学模型的建立与研究，国家自然科学基金项目（参加，项目编号：10471066；2005年1月-2007年12月）。

学术兼职

中国生物数学学会常务理事，《生物数学学报》常务编委，科学出版社《生物数学丛书》编委

学术论文

1. Ning Bai, Chenwei Song, Rui Xu*, Mathematical analysis and application of a cholera transmission model with waning vaccine-induced immunity, Nonlinear Analysis: Real World Applications 58 (2021) 103232.

2. Liangchen Li, Rui Xu*, Qintao Gan, Jiazhe Lin, Synchronization of neural networks with memristor-resistor bridge synapses and Lévy noise, Neurocomputing, 432 (2021) 262-274.

3. Chenwei Song, Rui Xu∗ and Ning Bai, Dynamics of a within-host virus infection model with multiple pathways: stability switch and global stability, International Journal of Bifurcation and Chaos, 31(13) (2021) 2150195.

4. Xiaomin Zhang, Rui Xu∗, Chenwei Song, Stability and Hopf bifurcation of a delayed viral infection dynamics model with immune impairment, International Journal of Bifurcation and Chaos, 31(8) (2021) 2150141.

5. Jiazhe lin, Rui Xu*, Spatio-temporal synchronization of reaction-diffusion BAMneural networks via impulsive pinning control, Neurocomputing, 418 (2020) 300-313.

6. Jiazhe Lin, Rui Xu*, Liangchen Li, Turing-Hopf bifurcation of reaction-diffusion neural networks with leakage delay, Commun Nonlinear Sci Numer Simulat. 85 (2020) 105241.

7. 白宁，宋晨玮，徐瑞*，基于动力学模型的COVID-19疫情预测与控制策略研究，应用数学学报，43(3)(2020) 483-493.

8. Junyuan Yang, Rui Xu*, Jiaxu Li, Threshold dynamics of an age–space tructured brucellosis disease model with Neumann boundary condition, Nonlinear Analysis: Real World Applications, 50 (2019) 192–217.

9. Rui Xu, Ning Bai and Xiaohong Tian, Global dynamics of a mathematical model of tuberculosis with age-dependent latency and active infection, Journal of Biological Systems, 27(4) (2019) 1–28.

10. Jiazhe Lin, Rui Xu*, Xiaohong Tian, Spatiotemporal dynamics in reaction– diffusion neural networks near a Turing–Hopf bifurcation point, International Journal of Bifurcation and Chaos, 29 (11) (2019) 1950154.

11. Jiazhe Lin, Rui Xu*, Liangchen Li, Effect of leakage delay on Hopf bifurcation in a fractional BAM neural network, International Journal of Bifurcation and Chaos, 29(6) (2019) 1950077.

12. Xiaohong Tian, Rui Xu*, Jiazhe Lin, Mathematical analysis of a cholera infection model with vaccination strategy, Applied Mathematics and Computation, 361 (2019) 517–535.

13. Jiazhe Lin, Rui Xu, Xiaohong Tian, Global dynamics of an age-structured cholera model with both human-to-human and environment-to-human transmissions and saturation incidence, Applied Mathematical Modelling, 63(2018)688-708.

14. Jiazhe Lin, Rui Xu, Xiaohong Tian, Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay and humoral immunity, Applied Mathematics and Computation, 315 (2017) 516–530.

15. Zhiping Wang, Rui Xu, Global dynamics of an SVIR epidemiological model with infection age and nonlinear incidence, Journal of Biological Systems, 25(3) (2017) 419–440.

16. Xiaohong Tian, Rui Xu, Stability and Hopf Bifurcation of time fractional Cohen- Grossberg neural networks with diffusion and time delays in leakage terms, Neural Processing Letters, 45(2017)593-614.

17. Jian Liu, Rui Xu, Delay-dependent passivity and stability analysis for a class of memristor-based neural networks with time delay in the leakage term, Neural Processing Letters, 46(2017) 467-485.

18. 陈辉, 徐瑞, 一类含潜伏期和CTL 免疫反应的病毒感染模型的全局渐近稳定性, 系统科学与数学，37(2) (2017) 632-640.

19. Xiaohong Tian, Rui Xu, Hopf Bifurcation analysis of a reaction-diffusion neural network with time delay in leakage terms and distributed delays, Neural Processing Letters, 43 (2016) 173-193.

20. Rui Xu, Zhili Wang, Fengqin Zhang, Global stability and Hopf bifurcations of an SEIR epidemiological model with logistic growth and time delay, Applied Mathematics and Computation, 269(2015) 332-342.

21. Xiaohong Tian, Rui Xu, Qintao Gan, Hopf bifurcation analysis of a BAM neural network with multiple time delays and diffusion, Applied Mathematics and Computation, 266(2015) 909-926.

22. Yanke Du, Rui Xu, Multistability and multiperiodicity for a class of Cohen- Grossberg bam neural networks with discontinuous activation functions and time delays, Neural Processing Letters, 42 (2015)417-435.

23. Rui Xu, Global dynamics of an SEIRI epidemiological model with time delay, Applied Mathematics and Computation, 232(2014)436-444.

24. Xiaohong Tian, Rui Xu, Global stability of a delayed HIV-1 infection model with absorption and CTL immune response, The IMA Journal of Applied Mathematics, 79(2014)347-359.

25. Xiaohong Tian, Rui Xu, Global stability and Hopf bifurcation of an HIV-1 infection model with saturation incidence and delayed CTL immune response, Applied Mathematics and Computation, 237 (2014) 146-154.

26. Yanke Du, Rui Xu, Robust synchronization of an array of neural networks with hybrid coupling and mixed time delays, ISA Transactions, 53(2014)1015-1023.

27. Rui Xu, Mathematical analysis of the global dynamics of an eco-epidemiological model with time delay, Journal of the Franklin Institute, 350(2013)3342-3364.

28. Rui Xu, Shihua Zhang, Modelling and analysis of a delayed predator-prey model with disease in the predator, Applied Mathematics and Computation, 224 (2013) 372-386.

29. Rui Xu, Global dynamics of an SEIS epidemiological model with time delay describing a latent period, Mathematics and Computers in Simulation, 85(2012) 90-102.

30. Rui Xu, Global stability of a delayed epidemic model with latent period and vaccination strategy, Applied Mathematical Modelling, 36 (2012)5293-5300.

31. Rui Xu, Global dynamics of an SEIS epidemic model with saturation incidence and latent period, Applied Mathematics and Computation, 218 (2012)7927-7938.

32. Rui Xu, Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response, Nonlinear Dynamics, 67(2) (2012) 1683- 1693.

33. Zhiping Wang, Rui Xu, Stability and Hopf bifurcation in a viral infection model with nonlinear incidence rate and delayed immune response, Communications in Nonlinear Science and Numerical Simulation, 17(2) (2012) 964-978.

34. Zhe Li, Rui Xu, Global asymptotic stability of stochastic reaction-diffusion neural networks with time delays in the leakage terms, Communications in Nonlinear Science and Numerical Simulation, 17 (2012) 1681-1689.

35. Qintao Gan, Rui Xu, Xibing Kang, Synchronization of unknown chaotic delayed competitive neural networks with different time scales based on adaptive control and parameter identification，Nonlinear Dynamics, 67(3)(2012) 1893-1902.

36. Qintao Gan, Rui Xu, Pinghua Yang, Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control, Communications in Nonlinear Science and Numerical Simulation, 17(1) (2012) 433-443.

37. Qintao Gan, Rui Xu, Pinghua Yang, Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion, Communications in Nonlinear Science and Numerical Simulation, 17(2012) 1862-1870.

38. Rui Xu, Global dynamics of a predator-prey model with time delay and stage structure for the prey, Nonlinear Analysis: Real World Applications, 12(2011) 2151-2162.

39. Rui Xu, Zhien Ma, Global dynamics of a vector disease model with saturation incidence and time delay, IMA Journal of Applied Mathematics, 76(6) (2011) 919- 937.

40. Rui Xu, Global dynamics of an HIV-1 infection model with distributed intracellular delays, Computers and Mathematics with Applications, 61 (2011) 2799-2805.

41. Rui Xu, Global Stability of an HIV-1 infection model with saturation infection and intracellular delay, Journal of Mathematical Analysis and Applications, 375 (2011) 75-81.

42. Rui Xu, Global convergence of a predator-prey model with stage structure and spatio-temporal delay, Discrete and Continuous Dynamical Systems, Series B, 15 (1) (2011) 273-291.

43. Qintao Gan, Rui Xu, Xibing Kang, Synchronization of unknown chaotic delayed competitive neural networks with different time scales based on adaptive control and parameter identification, Nonlinear Dynamics, 67 (2012)1893-1902.

44. Xiao Zhang, Rui Xu, Traveling waves of a diffusive predator-prey model with nonlocal delay and stage structure, Journal of Mathematical Analysis and Applications, 373 (2011) 475-484.

45. Qintao Gan, Rui Xu, Xibing Kang, Synchronization of chaotic neural networks with mixed time delays, Communications in Nonlinear Science and Numerical Simulation, 16(2)(2011) 966-974.

46. Qintao Gan, Rui Xu, Travelling waves of a delayed SIRS epidemic model with spatial diffusion, Nonlinear Analysis: Real World Applications, 12(2011) 52-68.

47. Qintao Gan, Rui Xu, Yanlu Li, Renxi Hu, Travelling waves in an infectious disease model with a fixed latent period and a spatio-temporal delay, Mathematical and Computer Modelling, 53(2011)814-823.

48. Rui Xu, Zhien Ma, Z. Wang, Global stability of a delayed SIRS epidemic model with saturation incidence and temporary immunity, Computers and Mathematics with Applications, 59(2010) 3211-3221.

49. Rui Xu，Zhien Ma，Global stability of a delayed SEIRS epidemic model with saturation incidence rate, Nonlinear Dynamics, 61(1-2)(2010)229-239.

50. Xiao Zhang, Rui Xu, Global stability and travelling waves of a predator-prey model with diffusion and nonlocal maturation delay, Communications in Nonlinear Science and Numerical Simulation, 15(2010) 3390-3401.

51. Qintao Gan, Rui Xu, Xiao Zhang, Pinghua Yang, Travelling waves of a three-species Lotka-Volterra food-chain model with spatial diffusion and time delays, Nonlinear Analysis: Real World Applications, 11(2010)2817-2832.

52. Qintao Gan, Rui Xu，Pinghua Yang, Zhen Wu, Travelling waves of a hepatitis B virus infection model with spatial diffusion and time delay，IMA J. Appl. Math. 75 (3) (2010) 392-417.

53. Qintao Gan, Rui Xu, Global robust exponential stability of uncertain neutral high- order stochastic Hopfield neural networks with time-varying delays, Neural Processing Letters, 32(1) (2010)83-96.

54. Qintao Gan, Rui Xu, Pinghua Yang, Stability analysis of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms, Neural Processing Letters, 32(1) (2010) 45-57.

55. Rui Xu, Zhien Ma, An HBV model with diffusion and time delay, Journal of Theoretical Biology, 257(3)(2009) 499-509.

56. Rui Xu, Zhien Ma, Global stability of a reaction-diffusion predator-prey model with a nonlocal delay, Mathematical and Computer Modelling, 50(1-2) (2009) 194-206.

57. Rui Xu, Zhien Ma, Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonlinear Analysis: Real World Applications, 10(5) (2009) 3175-3189.

58. Rui Xu, Qintao Gan, Zhien Ma, Stability and bifurcation analysis on a ratio-dependent predator-prey model with time delay, Journal of Computational and Applied Mathematics, 230(1) (2009) 187-203.

59. Yanke Du, Rui Xu, Lijiang Duan, Dynamics of a stage-structured predator-prey model concerning impulsive control strategy, Journal of Biological Systems, 17(4) (2009) 779-792.

60. Rui Xu, Zhien Ma, Qintao Gan, Stability and bifurcation in a Beddington- Deangelis predator-prey model with prey dispersal, Rocky Mountain J. Math. 38(5) (2008) 1761-1783.

61. Rui Xu, Zhien Ma, Stability and Hopf bifurcation in a predator-prey model with stage structure for the predator, Nonlinear Analysis: Real World Applications, 9(4) (2008) 1444-1460.

62. Rui Xu, Zhien Ma, The effect of dispersal on the permanence of a predator-prey system with time delay, Nonlinear Analysis: Real World Applications, 9(2) (2008) 354-369.

63. Rui Xu, Zhien Ma, The effect of stage-structure on the permanence of a predator- prey system with time delay, Applied Mathematics and Computation, 189 (2) (2007) 1164-1177.

64. Rui Xu, M.A.J. Chaplain, F.A. Davidson, Global convergence of a reaction- diffusion predator-prey model with stage structure and nonlocal delays, Computers and Mathematics with Applications, 53(5) (2007) 770-788.

65. Rui Xu, Z. Wang, Periodic solutions of a non-autonomous predator-prey system with stage structure and time delays, Journal of Computational and Applied Mathematics, 196(2) (2006) 70-86.

66. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Global convergence of a reaction- diffusion predator-prey model with stage structure for the predator, Applied Mathematics and Computation, 176(1) (2006)388-401.

67. Rui Xu, A reaction-diffusion predator-prey model with stage structure and nonlocal delay, Applied Mathematics and Computation, 175(2) (2006) 984-1006.

68. Rui Xu, M.A.J. Chaplain and F.A. Davidson, A Lotka-Volterra type food chain model with stage structure and time delays, Journal of Mathematical Analysis and Applications, 315(1) (2006)90-105.

69. Rui Xu, M.A.J. Chaplain, F.A. Davidson, Periodic solutions of a Lotka-Volterra type multi-species population model with time delays, Mathematische Nachrichten, 279 (8) (2006) 911-927.

70. 徐瑞，郝飞龙，陈兰荪，一个具有时滞和阶段结构的捕食模型，数学物理学报, 2006年第3期.

71. Rui Xu, Lansun Chen, Feilong Hao, Periodic solutions of a discrete time Lotka- Volterra type food-chain model with delays, Applied Mathematics and Computation, 171(1) (2005) 91-103.

72. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Global stability of a stage-structured predator-prey model with prey dispersal, Applied Mathematics and Computation, 171(1) (2005) 293-314.

73. Rui Xu, Lansun Chen, Feilong Hao, Periodic solutions of an n-species Lotka- Volterra type food-chain model with time delays, Applied Mathematics and Computation, 171(1) (2005) 511-530.

74. Rui Xu, M.A.J. Chaplain, F. Davidson, Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure, Journal of Mathematical Analysis and Applications, 303(1) (2005) 602-621.

75. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Periodic solutions for a predator- prey model with Holling-type functional response and time delays, Applied Mathematics and Computation, 161(2) (2005) 637-654.

76. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Modelling and analysis of a competitive model with stage structure, Mathematical and Computer Modelling, 41(2005) 159-175.

77. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments, Nonlinear Analysis: Real World Applications, 5(1) (2004) 183-206.

78. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Persistence and stability of a stage- structured predator-prey model with time delays, Applied Mathematics and Computation, 150(1) (2004) 259-277.

79. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Persistence and periodicity of a delayed ratio-dependent predator-prey model with stage structure and prey dispersal, Applied Mathematics and Computation, 159(3) (2004)823-846.

80. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay, Applied Mathematics and Computation, 159(3) (2004) 863-880.

81. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Persistence and global stability of a ratio-dependent predator-prey model with stage structure, Applied Mathematics and Computation, 158(3) (2004) 729-744.

82. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Periodic solutions of a predator-prey model with stage structure for predator, Applied Mathematics and Computation, 154(3) (2004) 847-870.

83. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Periodic solution for a three-species Lotka-Volterra food-chain model with time delays, Mathematical and Computer Modelling, 40(1-2) (2004)823-837.

84. Rui Xu, Lansun Chen, MAJ Chaplain, Persistence and global stability in a delayed predator-prey system with Holling-type functional response, ANZIAM Journal, 46 (1) (2004) 121-141.

85. Rui Xu, M.A.J. Chaplain and F.A. Davidson, Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays, Discrete and Continuous Dynamical Systems, Series B, 4(3) (2004) 823-831.

86. Rui Xu, Lansun Chen, MAJ Chaplain, Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with delays, Acta Mathematica Scientia, 23(2) (2003) 208-218.

87. Rui Xu, Lansun Chen, Persistence and global stability for n-species ratio- dependent predator-prey prey system with time delays, Journal of Mathematical Analysis and Applications, 275(1) (2002)) 27-43.

88. Rui Xu, Lansun Chen, Persistence and global stability for a three-species ratio- dependent predator-prey system with time delays in two-patch environments, Acta Mathematica Scientia, 22(4) (2002) 533-541.

89. Rui Xu, MAJ Chaplain, Persistence and attractivity in an N-species ratio- dependent predator-prey system with distributed time delays, Applied Mathematics and Computation, 131(1) (2002) 59-80.

90. Rui Xu, MAJ Chaplain, Chen LS, Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with infinite delays, Applied Mathematics and Computation, 130(2-3) (2002) 295-309.

91. Rui Xu, MAJ Chaplain, Persistence and global stability in a delayed predator-prey system with Michaelis-Menten type functional response, Applied Mathematics and Computation, 130(2-3) (2002) 441-455.

92. Rui Xu, FA Davidson, MAJ Chaplain, Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time delay, Journal of Mathematical Analysis and Applications, 269(1) (2002) 256-277.

93. FA Davidson, Rui Xu, Liu J, Existence and uniqueness of limit cycles in an enzyme-catalysed reaction system, Applied Mathematics and Computation, 127 (2-3) (2002) 165-179.

94. Rui Xu, MAJ Chaplain, Persistence and global stability in a delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks, Journal of Mathematical Analysis and Applications, 265(1) (2002) 148-162.

95. Rui Xu, Lansun Chen, Persistence and global stability for a delayed nonautonomous predator-prey system without dominating instantaneous negative feedback, Journal of Mathematical Analysis and Applications, 262(1)(2001)50- 61.

96. 徐瑞，陈兰荪，具有时滞和基于比率的三种群捕食系统的全局稳定性,系统科学与数学，21(2)(2001) 204-212.

97. Rui Xu, Lansun Chen, Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment, Computers and Mathematics with Applications, 40(4-5) (2000) 577-588.

98. Yang Pinghua, Xu Rui, Global attractivity of the periodic Lotka-Volterra system, Journal of Mathematical Analysis and Applications, 233(1999) 221-232.