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   Research

Research Interests

  • Differential Equations and Dynamical Systems
  • Mathematical Biology
  • Applied Mathematics

 

Projects supported by NSF

         DEB-1021203: Collaborative Research: Vulnerable Host Stages, Development Time, and Host-Parasitoid Stability - The First Experimental Test. PI: J. D. Reeve, Co-PI: M. Xiao, D. Xu.

         DMS-0719783: Collaborative Research: Modeling Complex Dynamics of Host-Parasite Interactions. PI: D. Xu.

Publications

1       L. Wang, D. Zhou, Z. Liu, D. Xu and X. Zhang, 2016. Media alert in an SIS epidemic model with logistic growth. J. of Biological Dynamics. DOI: 10.1080/17513758.2016.1181212.

2       Y. Chang, X. Wang and D. Xu, 2016. Bifurcation analysis of a power system model with three machines and four buses. I. J. of Bifurcation and Chaos, 26(5):1650082. DOI: 10.1142/S0218217416500826.

3       J. T. Cronin, J. D. Reeve, D. Xu, M. Xiao and H. N. Stevens, 2016. Variable prey development time suppresses predator-prey cycles and enhances stability. Ecology Letters, 19: 318-327. DOI: 10.1111/ele.12572. On-line supplementary material.

4       X. Wang, Y. Chang and D. Xu, 2015. Bifurcation analysis of a Belousov-Zhabotinsky reaction model. I. J. of Bifurcation and Chaos, 25(6). DOI: 10.1142/S0218127415500935.

5       F. Rong, D. Meng and D. Xu, 2014. Survey of research process on statistical correlation analysis. Mathematical Modeling and Its Applications, 3(1): 1-12. (in Chinese, with an English abstract at the end of the paper)

6       M-Q Xiao, J. D. Reeve, D. Xu, J. T. Cronin, 2013. Estimation of the diffusion rate and crossing probability for biased edge movement between two different types of habitat. J. Mathematical Biology, 67: 535-567.

7       D. Xu, D. J. Minchella, G. J. Sandland, Z. Feng, 2012. Interactions among virulence, coinfection and drug resistance in a complex life-cycle parasite. J. Theoretical Biology, 304: 197-210.

8       Y. Yang, Z. Feng, D. Xu, G. Sandlandm D. J. Minchella, 2012. Evolution of host resistance to parasite infection in the snail-schistosome-human system. J. Mathematical Biology, 65: 201-236.

9       A. Min, J. D. Reeve, M. Xiao, D. Xu, 2012. Identification of diffusion coefficient in nonhomogeneous landscapes. Lecture Notes in Computer Sciences, Springer, vol. 7664, pp. 290-297.

10  Y. Zhang, S. Wang, M. Yang, D. Xu and D. Meng, 2011. A new method of determining threshold of gene network based on phenotypes. Journal of Biological Systems, 19(4): 607-616.

11  S. Wang, K. Li, X. Xu, D. Meng and D. Xu, 2011. Structural characteristics of gene networks for colon cancer. 2011 IEEE International Conference on Signal Processing, Communications and Computing. DOI: 10.1109/ICSPCC.2011.6061817. http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=6061817

12  D. Xu, J. D. Reeve, X. Wang, M-Q Xiao, 2010. Developmental variability and stability in continuous-time host-parasitoid models. Theoretical Population Biology, 78: 1-11.

13  D. Xu and Z. Feng, 2009. A metapopulation model with local competitions, Discrete and Continuous Dynamical Systems (Series B), 12(2): 495-511.

14  Z. Feng, Y. Yang, D. Xu, P. Zhang, M. McCauley, M., J. W. Glasser, 2009. Timely identification of optimal control strategies for emerging infectious diseases, J. Theoretical Biology, 259: 165-171.

15  C. Castillo-Chavez, Z. Feng and D. Xu, 2008. A schistosomiasis model with mating structure and time delay, Mathematical Biosciences, 211, 333-341.

16  Y. Yang, D. Xu, Z. Feng, 2008. Analysis of a model with multiple infectious stages and arbitrarily distributed stage durations, Math. Model. Nat. Phenom. 3(7), 180-193.

17  Z. Feng, D. Xu, H. Zhao. Epidemiological models with non-exponentially distributed disease stages and applications to disease control, Bulletin of Mathematical Biology, 69 (5), 1511-1536, 2007.

18  P. Zhang, G. Sandland, Z. Feng, D. Xu, D. J. Minchella. Evolutionary implications for interactions between multiple strains of host and parasite, J. Theoretical Biology, 248, 225-240, 2007.

19  D. Xu, Z. Feng, L. Allen and R. K. Swihart. A spatially structured metapopulation model with patch dynamics, J. Theo. Bio., 239, 469-481, 2006.

20  D. Xu, J. Curtis, Z. Feng and D. J. Minchella. On the role of schistosome mating structure in the maintenance of resistant strains, Bulletin for Math. Bio., 67: 1207-1226, 2005.

21  D. Xu, X.-Q. Zhao. Dynamics in a periodic competitive model with stage structure, J. Math. Anal. Appl., 311: 417-438, 2005.

22  D. Xu, X.-Q. Zhao. Asymptotic speed of spread and traveling waves for a nonlocal epidemic model, Discrete Contin. Dynam. Systems, 5: 1043-1058, 2005.

23  D. Xu. Global dynamics and Hopf bifurcation of a structured population model, Nonlinear Analysis: Real World Applications, 6: 461-476, 2005.

24  D. Xu, X.-Q. Zhao. Bistable waves in an epidemic model, J. of Dynamics and Differential equations, 16: 679-707, 2004.

25  D. Xu, X.-Q. Zhao. A nonlocal reaction-diffusion population model with stage structure, Canad. Appl. Math. Quart., 11: 303-319, 2003.

26  Z. Jing, D. Xu, Y. Chang, L. Chen. Bifurcations, chaos, and system collapse in a three-node power system, International J. of Electrical Power Energy Systems, 25, 443-461, 2003.

27  Z. Jing, K. Y. Chan, D. Xu, H. Cao. Bifurcations of periodic solutions and chaos in Josephson system, Discrete Contin. Dynam. Systems, 7(3): 573-592, 2001.

28  D. Xu, D. Meng. The model and simulation of inhibition in the extrinsic path of blood coagulation: the dynamic effects of protein C, Acta Biophysica Sinica, 14: 657-665, 1998. (Chinese)

Finished or on-going projects

         The role of tuberculosis in high HIV prevalence populations. In preparation (with Z. Feng and M. Lannelli).

 

Curriculum Vitae

 

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 Last modified Apr., 2016 by Dashun Xu..