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教 授
徐瑞

徐瑞,山西大学复杂系统研究所教授、博士生导师

Education
PhD (2002-2005), Mathematical Biology, The University of Dundee, UK
MSc (1985-1987), Applied Mathematics, Xian Jiaotong University, China
BSc (1981-1985), Mathematics, Hebei Normal University, China

Research Interests:
Mathematical Biology
Epidemiological Modeling
Theoretical Ecology

Address:
Complex Systems Research Center
Shanxi University
Taiyuan 030006, Shanxi, P.R. China

Shanxi Key Laboratory of Mathematical Techniques and
Big Data Analysis on Disease Control and Prevention,
Shanxi University, Taiyuan 030006, Shanxi, P.R. China

E-mail:
rxu88@163.com
xurui@sxu.edu.cn

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,美国《数学评论》和德国《数学文摘》评论员。

Funded research projects
(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(与南京师范大学崔景安教授合作申请,项目编号:10471066;2005年1月-2007年12月)。
(6)具有类年龄结构的传染病动力学的建模与研究,河北省自然科学基金项目(项目负责人;项目编号:A2014506015;2014年1月-2016年12月)。
(7)具有时空滞后效应的反应扩散生物种群动力学模型的建立与研究,中国博士后科学基金项目(项目负责人;项目编号:20060391010;2006年10月-2008年10月)。
(8)具有时空滞后的反应扩散种群模型的建立与研究,教育部留学回国人员科研启动基金(项目负责人;项目编号:教外司留字[2007](1108))。

指导研究生情况:
指导博士研究生11人。指导的研究生获全军优秀博士学位论文1篇,河北省优秀博士学位论文2篇,总装备部优秀博士学位论文2篇,河北省或总装备部优秀硕士学位论文4篇。

出版著作:
甘勤涛,徐瑞,时滞神经网络的稳定性与同步控制,科学出版社,2016年1月。
 

发表的主要论文
[1] 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 (SCI).
[2] Jian Liu and Rui Xu, Adaptive synchronisation ofmemristor-based neural networks with leakage delays and applications in chaoticmasking secure communication, International Journal of Systems Science, 49(6)1300-1315 (SCI).
[3] Rui Xu, Xiaohong Tian and Shihua Zhang, An age-structured within-host HIV-1 infection model with virus-to-cell and cell-to-cell transmissions, Journal of Biological Dynamics, 12(1)(2018)89-117 (SCI).
[4] Rui Xu, Global dynamics of an epidemiological model with age of infection and disease relapse, Journal of Biological Dynamics, 12(1) (2018)118-145.
[5] 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 (SCI)
[6] Jian Liu, Rui Xu, Global dissipativity analysis for memristor-based uncertain neural networks with time delay in the leakage term, International Journal of Control, Automation and Systems 15(5) (2017) 2406-2415 (SCI, EI)
[7] 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 (SCI)
[8] Rui Xu, Shihua Zhang, Fengqin Zhang, Global dynamics of a delayed SEIS infectious disease model with logistic growth and saturation incidence response, Mathematical Methods in the Applied Sciences, 39(2016)3294-3308 (SCI)
[9] Xiaohong Tian, Rui Xu, Stability and Hopf bifurcation of a delayed Cohen- Grossberg neural network with diffusion, Math. Meth. Appl. Sci. 40(2017)293-305(SCI)
[10] 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 (SCI)
[11] Hui Chen, Rui Xu, Stability and bifurcation analysis of a viral infection model with         delayed immune response, Journal of Applied Analysis and Computation, 7(2)(2017)532-553(SCI)
[12] 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(SCI)
[13] 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 (SCI)
[14] Lili Wang, Rui Xu, Global stability of an SEIR epidemic model with vaccination, International Journal of Biomathematics, 9(6) (2016), 1650082 (23 pages) (SCI)
[15] Lingshu Wang, Rui Xu, G. Feng, Modelling and analysis of an eco-epidemiological model with time delay and stage structure, Journal of Applied Mathematics and Computing, 50 (1)(2016)175-197 (EI)
[16] 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 (SCI)
[17] 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(SCI)
[18] Xiaohong Tian, Rui Xu, Global stability and Hopf bifurcation of a delayed eco-epidemiological model with Holling type II functional response, Mathematical Methods in the Applied Sciences, 38(2015)4416-4434 (SCI)
[19] Haibin Wang, Rui Xu, Zhaowei Wang, Hui Chen, Global Dynamics of a class of HIV-1 infection models with latently infected cells, Nonlinear Analysis: Modelling and Control, 20(1) (2015)21-37 (SCI)
[20] 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 (SCI)
[21] Shihua Zhang, Global stability of a delayed ratio-dependent predator-prey model with Gompertz growth for prey, Journal of Applied Analysis and Computation, 5(1) (2015) 28-37(SCI)
[22] Lingshu Wang, Rui Xu, G. Feng, Global dynamics of a delayed predator-prey model with stage structure and Holling type II functional response, J. Appl. Math. Comput. 47 (2015)73-89 (EI)
[23] Rui Xu, Global dynamics of an SEIRI epidemiological model with time delay, Applied Mathematics and Computation, 232(2014)436-444 (SCI)
[24] Rui Xu, Xiaohong Tian, Stability and Hopf bifurcation of a delayed epidemic model with stage structure and nonlinear incidence rate, Mathematical Methods in the Applied Sciences, 37(2014) 2150-2163 (SCI)
[25] Rui Xu, Xiaohong Tian, Global dynamics of a delayed eco-epidemiological model with Holling type-III functional response, Mathematical Methods in the Applied Sciences, 37(2014) 2120-2134 (SCI:000340424800006)
[26] Xiaohong Tian, Rui Xu, Stability analysis of an SEIS epidemic model with nonlinear incidence and time delay, Journal of Applied Analysis and Computation, 4(4)(2014)405-418(SCI)
[27] 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 (SCI)
[28] 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 (SCI)
[29] Zhiping Wang and Rui Xu, Stability and traveling waves of an epidemic model with relapse and spatial diffusion, Journal of Applied Analysis and Computation, 4(3)(2014)307-322 (SCI)
[30] 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 (SCI)
[31] Rui Xu, Global dynamics of a delayed epidemic model with latency and relapse, Nonlinear Analysis: Modelling and Control, 18(2) (2013) 250-263 (SCI)
[32] 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(SCI)
[33] 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(SCI)
[34] Shihua Zhang, Rui Xu, Travelling waves and global attractivity of an SIRS disease model with spatial diffusion and temporary immunity, Applied Mathematics and Computation, 224(2013)635-651 (SCI)
[35] Zhiping Wang, Rui Xu, Traveling waves of an epidemic model with vaccination, International Journal of Biomathematics, 6(5)(2013), 1350033,19 pages (SCI)
[36] Yanke Du, Rui Xu, Qiming Liu, Stability and bifurcation analysis for a neural network model with discrete and distributed delays, Math. Meth. Appl. Sci. 36(2013)49-59 (SCI)
[37] 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 (SCI:000312628100007)
[38] Rui Xu, Global stability of a delayed epidemic model with latent period and vaccination strategy, Applied Mathematical Modelling, 36 (2012)5293-5300 (SCI: 000309082400011)
[39] Rui Xu, Global dynamics of a delayed HIV-1 infection model with absorption and saturation infection, International Journal of Biomathematics, 5(3) (2012), 1260012 (13pages) (SCI: 000303395000012)
[40] Rui Xu, Global dynamics of an SEIS epidemic model with saturation incidence and latent period, Appl. Math. Comput. 218 (2012)7927-7938 (SCI: 000301455300026)
[41] 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 (SCI: 000297820100057)
[42] Zhe Li, Rui Xu, Traveling waves in a reaction-diffusion predator-prey system with nonlocal delays, International Journal of Biomathematics, 5(5)(2012), 1250043 (19 pages)(SCI: 000305481900009)
[43] 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 (SCI)
[44] Yanke Du and Rui Xu, Traveling wave solutions in a three-species food-chain model with diffusion and delays, International Journal of Biomathematics, 5(1)(2012), 1250002 (17 pages) (SCI: 000300251100002)
[45] 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(SCI:000297893800019)
[46] L. Wang and Rui Xu, Mathematical analysis of an improved hepatitis B virus model, International Journal of Biomathematics, 5(1) (2012), 1250006 (18 pages) (SCI: 000300251100006)
[47] 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 (SCI: 000299085800018)
[48] 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 (SCI:000295995300042)
[49] 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 (SCI: 000297893800036)
[50] 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 (SCI: 000291196000024)
[51] 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 (SCI: 000296635400007)
[52] Rui Xu, Global dynamics of an HIV-1 infection model with distributed intracellular delays, Computers and Mathematics with Applications, 61 (2011) 2799-2805 (SCI: 000291069600046)
[53] Rui Xu, Global Stability of an HIV-1 infection model with saturation infection and intracellular delay, J. Math. Anal. Appl. 375 (2011) 75-81 (SCI: 000284293600007)
[54] 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 (SCI: 000283558300014)
[55] Rui Xu, Yanke Du, A delayed SIR epidemic model with saturation incidence and a constant infectious period, Journal of Applied Mathematics and Computing, 35(2011)229-250 (EI: 20110313590191)
[56] Xiaohong Tian, Rui Xu, Global dynamics of a predator-prey system with Holling type II functional response, Nonlinear Analysis: Modelling and Control, 16(2) (2011) 242-253 (SCI: 000293384500010)
[57] Qiming Liu, Rui Xu, Stability and bifurcation of a Cohen-Grossberg neural network with discrete delays, Appl. Math. Comput.  218(6) (2011) 2850-2862 (SCI: 000296278800043)
[58] 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 (SCI)
[59] 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 (SCI: 000282353900015)
[60] 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 (SCI:000282533900037)
[61] Qintao Gan, Rui Xu, Travelling waves of a delayed SIRS epidemic model with spatial diffusion, Nonlinear Analysis: Real World Applications, 12(2011) 52-68 (SCI: 000284292000006)
[62] 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(SCI:000286458200029)
[63] Xiao Zhang, Rui Xu, Zhe Li, Global stability of a three-species food-chain model with diffusion and nonlocal delays, Mathematical Modelling and Analysis, 16(3) (2011) 376-389 (SCI: 000294519800003)
[64] Qintao Gan, Rui Xu, Stability and Hopf bifurcation of a delayed reaction-diffusion neural network, Mathematical Methods in the Applied Sciences, 34(12)(2011) 1450-1459 (SCI:000293751200005)
[65] Qiming Liu, Rui Xu, Periodic solutions of high-order Cohen-Grossberg neural networks with distributed delays, Commun Nonlinear Sci Numer Simulat, 16(7) (2011)2887-2893 (SCI:000288639900023)
[66] Rui Xu, Zhien Ma, Z. Wang, Global stability of a delayed SIRS epidemic model with saturation incidence and temporary immunity, Comput. Math. Appl. 59(2010) 3211-3221(SCI:000277850400020)
[67] Rui Xu,Zhien Ma,Global stability of a delayed SEIRS epidemic model with saturation incidence rate, Nonlinear Dynamics, 61(1-2)(2010)229-239 (SCI: 000279478400019)
[68] Xiao Zhang, Rui Xu, Global stability and travelling waves of a predator-prey model with diffusion and nonlocal maturation delay, Commun Nonlinear Sci Numer Simulation, 15(2010) 3390-3401 (SCI: 000278723500022)
[69] 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(SCI)
[70] 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 (SCI)
[71] 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 (SCI)
[72] 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 (SCI)
[73] Zhe Li, Rui Xu, Stability analysis of a ratio-dependent chemostat model with time delay and variable yield, International Journal of Biomath. 3(2) (2010) 243-253 (SCI: 000279192500007)
[74] Rui Xu, Zhien Ma, An HBV model with diffusion and time delay, J. Theoretical Biol. 257(3)(2009) 499-509 (SCI)
[75] Rui Xu, Zhien Ma, Global stability of a reaction-diffusion predator-prey model with a nonlocal delay, Math. Comput. Modelling, 50(1-2)(2009) 194-206(SCI)
[76] Rui Xu, Zhien Ma, Stability of a delayed SIRS epidemic model with a nonlinear incidence rate, Chaos, Solitons & Fractals, 41(5)(2009) 2319-2325 (SCI)
[77] Rui Xu, Zhien Ma, Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonlinear Anal. RWA, 10(5) (2009) 3175-3189 (SCI)
[78] Rui Xu, Qintao Gan, Zhien Ma, Stability and bifurcation analysis on a ratio-dependent predator-prey model with time delay, J. Comput. Appl. Math.  230(1) (2009)187-203 (SCI)
[79] Qintao Gan, Rui Xu, Wenhua Hu, Pinghua Yang, Bifurcation analysis for a tri-neuron discrete-time BAM neural network with delays, Chaos, Solitons & Fractals, 42(4)(2009) 2502-2511 (SCI)
[80] Qintao Gan, Rui Xu, Pinghua Yang, Bifurcation and chaos in a ratio-dependent predator-prey system with time delay, Chaos, Solitons & Fractals, 39(4)(2009) 1883-1895 (SCI)
[81] Y. Du, Rui Xu, L. Duan, Dynamics of a stage-structured predator-prey model concerning impulsive control strategy, J. Biol. Systems, 17(4) (2009) 779-792(SCI)
[82] L. Wang, Rui Xu, G. Feng, Stability and Hopf bifurcation of a predator-prey system with time delay and Holling type-II functional response, International Journal of Biomath. 2(2) (2009)139-149 (SCI: 000279191400003).
[83] Rui Xu, Zhien Ma, Stability and Hopf bifurcation in a ratio-dependent predator-prey system with stage structure, Chaos, Solitons & Fractals, 38(3)(2008) 669-684 (SCI)
[84] 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 (SCI)
[85] Rui Xu, Zhien Ma, Stability and Hopf bifurcation in a predator-prey model with stage structure for the predator, Nonlinear Anal. RWA, 9(4) (2008) 1444-1460 (SCI)
[86] Rui Xu, Zhien Ma, The effect of dispersal on the permanence of a predator-prey system with time delay, Nonlinear Anal. RWA, 9(2) (2008) 354-369 (SCI)
[87] Qintao Gan; Rui Xu; Pinghua Yang, Bifurcation analysis for a predator-prey system with prey dispersal and time delay, International J. Biomath. 1(2) (2008) 209-224 (SCI: 000207588100009)
[88] Rui Xu, Zhien Ma, The effect of stage-structure on the permanence of a predator- prey system with time delay, Appl. Math. Comput. 189 (2) (2007) 1164-1177 (SCI)
[89] Rui Xu, M.A.J. Chaplain, F.A. Davidson, Global convergence of a reaction-diffusion predator-prey model with stage structure and nonlocal delays, Comput. Math. Appl. 53(5) (2007) 770-788 (SCI)
[90] Rui Xu, Z. Wang, Periodic solutions of a non-autonomous predator-prey system with stage structure and time delays, J. Comput. Appl. Math. 196(2) (2006) 70-86 (SCI)
[91] Rui Xu, MAJ Chaplain, FA Davidson, Global convergence of a reaction-diffusion predator- prey model with stage structure for the predator, Appl. Math. Comput.  176(1) (2006)388-401 (SCI)
[92] Rui Xu, MAJ Chaplain, FA Davidson, Travelling wave and convergence in stage- structured reaction-diffusion competitive models with nonlocal delays, Chaos, Solitons & Fractals, 30(4)(2006) 974-992 (SCI)
[93] Rui Xu, A reaction-diffusion predator-prey model with stage structure and nonlocal delay, Appl. Math. Comput. 175(2) (2006) 984-1006 (SCI)
[94] Rui Xu, M.A.J. Chaplain and F.A. Davidson, A Lotka-Volterra type food chain model with stage structure and time delays, J. Math. Anal. Appl. 315(1) (2006)90-105 (SCI)
[95] 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 (SCI)
[96] Rui Xu, Zhien Ma, F. Hao, P. Yang, Global stability of a delayed predator-prey model with stage structure for the prey, Indian J. Pure Appl. Math. 37(5) (2006) 273-289 (SCI)
[97] Rui Xu, Lansun Chen, Feilong Hao, Periodic solutions of a discrete time Lotka-Volterra type food-chain model with delays,  Appl. Math. Comput. 171(1) (2005) 91-103 (SCI)
[98] Rui Xu, MAJ Chaplain, FA Davidson, Global stability of a stage-structured predator-prey model with prey dispersal, Appl. Math. Comput. 171(1) (2005) 293-314 (SCI)
[99] Rui Xu, L. Chen, Feilong Hao, Periodic solutions of an n-species Lotka-Volterra type food-chain model with time delays, Appl. Math. Comput. 171(1) (2005) 511-530 (SCI)
[100] Rui Xu, M.A.J.Chaplain, F. Davidson, Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure, J. Math. Anal. Appl. 303(1) (2005) 602-621(SCI)
[101] 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, Appl. Math. Comput. 161(2) (2005) 637-654 (SCI)
[102] Rui Xu, MAJ Chaplain, FA Davidson, Modelling and analysis of a competitive model with stage structure, Math. Comput. Modelling, 41(2005) 159-175 (SCI)
[103] Rui Xu, Chaplain MAJ, Davidson FA, Periodic solutions for a delayed predator- prey model of prey dispersal in two-patch environments, Nonlinear Anal. RWA, 5(1) (2004) 183-206 (SCI)
[104] Rui Xu, Chaplain MAJ, Davidson FA, Persistence and stability of a stage-structured predator-prey model with time delays, Appl. Math. Comput. 150(1) (2004) 259-277(SCI)
[105] 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,  Appl. Math. Comput. 159(3) (2004)823-846 (SCI)
[106] Rui Xu, Chaplain MAJ, Davidson FA, Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay,  Appl. Math. Comput. 159(3) (2004) 863-880 (SCI)
[107] Rui Xu, MAJ Chaplain and FA. Davidson, Persistence and global stability of a ratio-dependent predator-prey model with stage structure, Appl. Math. Comput.  158(3) (2004) 729-744 (SCI)
[108] Rui Xu, MAJ Chaplain and FA. Davidson, Periodic solutions of a predator-prey model with stage structure for predator, Appl. Math. Comput. 154(3) (2004) 847-870 (SCI)
[109] Rui Xu, M.A.J. Chaplain and F.A. Davidson, Periodic solution for a three-species Lotka-Volterra food-chain model with time delays,  Math. Comput. Modelling, 40(1-2) (2004)823-837 (SCI)
[110] 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 (SCI)
[111] Rui Xu, MAJ Chaplain, FA Davidson, Global asymptotic stability of a periodic solution for a cooperative system with time delays, Indian J. Pure and Appl. Math. 35(7) (2004) 915-936 (SCI)
[112] Rui Xu, M.A.J. Chaplain, F.A. Davidson, Periodic solutions of a discrete non-autonomous Lotka-Volterra predator-prey model with time delays, Discrete and Continuous Dynamical Systems, Series B, 4(3)(2004) 823-831 (SCI)
[113] Rui Xu, Chen L., Chaplain MAJ, Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with delays, Acta Mathematica Scientia, 23(2)(2003) 208-218 (SCI)
[114] Rui Xu, Chen LS, Persistence and global stability for n-species ratio-dependent predator-prey prey system with time delays, J. Math. Anal. Appl. 275(1) (2002)) 27-43 (SCI)
[115] Rui Xu, Chen L.S., 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 (SCI)
[116] Rui Xu, Chaplain MAJ, Persistence and attractivity in an N-species ratio-dependent predator-prey system with distributed time delays, Appl. Math. Comput. 131(1) (2002) 59-80 (SCI)
[117] Rui Xu, Chaplain MAJ, Chen LS, Global asymptotic stability in n-species non-autonomous Lotka-Volterra competitive systems with infinite delays, Appl. Math. Comput. 130(2-3) (2002) 295-309 (SCI)
[118] Rui Xu, Chaplain MAJ, Persistence and global stability in a delayed predator-prey system with Michaelis-Menten type functional response, Appl. Math. Comput. 130(2-3) (2002) 441-455 (SCI)
[119] Rui Xu, Davidson FA, Chaplain MAJ, Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time delay, J. Math. Anal. Appl. 269(1) (2002) 256-277 (SCI)
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