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Research Interests

               Differential Equations and Dynamical Systems

               Mathematical Biology

               Applied Mathematics

Current research (supported by NSF-1021203):

       A collaborative research with James Cronin, John Reeve and Mingqing Xiao: Development time and predator-prey population dynamics.

Publications (paper available upon email requests)

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

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

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

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

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

6.      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.

7.      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.

8.      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.

9.      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.

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

11.  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.

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

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

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

15.  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.

16.  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.

17.  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

         M.-Q. Xiao, J. D. Reeve and D. Xu. Mean occupancy time for biased edge movement between two different habitat types. Submitted, 2010. (the paper available upon email requests)

         Y. Chang, D. Xu and Z. Jing. Complex dynamics in swing equations of a power system model. Submitted 2010. (the paper available upon email requests)

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

         The role of drug treatments in the evolutionary dynamics of complex host-parasite interactions. In preparation (with Z. Feng, G. Sandland, D. J. Minchella, Y. Yang).

 

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 Last modified Aug., 2010 by Dashun Xu..