Research Interests:

Differential equations (PDEs, ODEs and FDEs), difference equations, applied dynamical systems, mathematical biology, neural networks. Why these ?
• Things are changing in the real world, and differential equations are equations involing derivatives which are rates of changes. This is why differential equations are so important in understanding many changing phenomenons in nature, including those in biology, physics, and even economics and finance. And this is also why I am interested in DEs and their applications.
• It is commonly agreed that much of the mathematics in the 20th century was driven by physiscs. Now it is also widely believed that much of the mathematics in this century will be driven by biology---there are so many biological questions that can not be answered merely by biologists. It is high time for applied mathematicians to get in.
  
  Among my works on applications of DEs to biological problems is the following example:
  Analytically Solving the Beetle Problem (Stephen A. Gourley and X. Zou, SIAM J Appl. Math., 68(2008), 1665-1687).
  This work has received A Nugget from SIAM , it has als been selected to republish, as a SIGEST paper in SIAM Reviews (SIAM Rev. 53(2011), 321-345).

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Awards and Honors:

• Distinguished Research Professorship (2011)
• Premier's Research Excellence Award (2005)
• Petro-Canada Young Innovator Award (2002)
• NSERC Postdoctoral Fellowship (1997-1999)

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Funding (I am grateful to all these programs/agents from which I have received funding):

• Ontario Ministry of Natural Resources (2011-2014)
• NSERC Discovery Accelerator Supplements (2010-2013)
• NSERC Discovery (2010-2015)
• Ontario Ministry of Science, Technology and Industry (PREA, 2005-2010)
• NSERC Discovery (2005-2010)
• Fields Institute (with L. Wahl and G. Webb, 2005)
• NSF (USA) (with L. Wahl and G. Webb, 2005)
• MITAC-NCE (with J. Watmough et al, 2005--2008, 2008---2012)
• University of Western Ontario (Start-up, 2004-2006)
• AARMS, Fields Institute and CRM (with H. Brunner and X.-Q. Zhao, 2004)
• Petro-Canada (Young Innovator Award)(2002-2004)
• NSERC Discovery (2000-2005)
• MITAC-NCE Fund (with S. Campbell et al, 1999-2002)
• CFI (with D. Pike et al, 1999)
• Memorial University of Newfoundland (Start-up, 1999-2002)

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Selected Publications (updated Jan 2004) : [Full list of Publications]

1. Dynamics of a non-autonomous ratio-dependent predator-prey system (with M. Fan and Q. Wang), Proc. Royal Soc. Edinb. A, 133 (2003), 97-118.
   
2. 3/2-type criteria for global attractivity of Lotka-Volterra competition system without instantaneous negative feedbacks (with X.-H. Tang), J. Differential Equations, 186(2002), 420-439.
   
3. Periodic solutions of neutral functional differential equations (with L. Wang and Z. Wang), J. London Math. Soc., 65 (2002), 439-452.
   
4. Delay induced traveling wave fronts in reaction diffusion equations of KPP-Fisher type, J. Comput. Appl. Math., 146 (2002), 309-321.
   
5. Exponential stability of Cohn-Grossburg neural network (with L. Wang), Neural Networks, 15 (2002), 415-422.
   
6. A reaction diffusion model for a single species with age structure ---I. Traveling wave fronts on unbounded domains (with J. So and J. Wu), Proc. Royal Soc. London. A, 457(2001), 1841-1854.
   
7. Stabilization role of inhibitory self-connections in a delayed neural network (with P. van den Driessche and J. Wu), Physica D., 150(2001), 84-90.
   
8. Traveling wave front solutions in reaction-diffusion systems with delay (with J. Wu), J. Dynamics and Differential Equations, 13(2001), 651-687.
   
9. Interaction of maturation delay and nonlinear birth in population and epidemic models (with K. Cooke and P. van den Driessche), J. Math. Biol., 39(1999), 332-352.
   
10. Global attractivity in delayed Hopfield neural network models (with P. van den Driessche), SIAM J. Appl.Math., 58:6(1998), 1978-1890.
    
11. Existence of traveling wave fronts in delayed reaction-diffusion systems via monotone iteration method (with J. Wu), Proc. Amer. Math. Soc., 125(1997), 2589-2598.
    
12. Local-nonlocal interaction and spatio-temporal patterns in single-species population over a patch environment (with N. Madras and J. Wu), Canad. Appl. Math. Quart., 4:1(1996), 109-134.