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.
- 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.
15. 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.
16. 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).
Vita
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