Equations and Dynamical Systems
Projects supported by NSF
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.
Collaborative Research: Modeling Complex
Dynamics of Host-Parasite Interactions. PI: D. Xu.
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:
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.
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.
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:
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)
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.
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.
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.
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.
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.
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
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.
D. Xu and Z. Feng, 2009. A metapopulation
model with local competitions, Discrete and Continuous Dynamical
Systems (Series B), 12(2): 495-511.
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.
C. Castillo-Chavez, Z. Feng and D. Xu,
2008. A schistosomiasis
model with mating structure and time delay, Mathematical
Biosciences, 211, 333-341.
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.
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.
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,
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.
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:
D. Xu, X.-Q. Zhao. Dynamics in a periodic competitive model with
stage structure, J. Math. Anal. Appl., 311: 417-438, 2005.
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.
D. Xu. Global
dynamics and Hopf bifurcation of a structured
population model, Nonlinear Analysis: Real World Applications, 6:
D. Xu, X.-Q. Zhao. Bistable waves
in an epidemic model, J. of Dynamics and Differential equations,
16: 679-707, 2004.
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.
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.
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)
The role of tuberculosis in high HIV
prevalence populations. In preparation (with Z. Feng and M. Lannelli).