Functional differential equations; Dynamical systems; Matrix and tensor analysis; Neural networks; Mathematical biology.

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1. 2009--2014: NSERC Research Grant: Dynamics of Delay Differential Equations: Theory and Applications.
2. September 20, 2005--December 31, 2011: Early Researcher Award.
3. 2004--2009: NSERC Research Grant: Dynamics of Systems of Delay-Differential Equations.
4. 2002--2004: NSERC Research Grant: Dynamics of Delay-differential Systems Describing Neural Networks.
5. 2001--2004: Start-up Fund from Wilfrid Laurier University.

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1. The Foruth International Conference on Recent Advances in Applied Dynamical Systems, Zhejiang Normal University, Jinhua, Zhejiang Province, P.R. China, June 16-20, 2010.  

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2011

63. "Traveling wavefronts pf a prey-predator diffusion system with stage-structure and harvesting", J. Comput. Appl. Math., 235 (2011) 2560-2568. (with X. Liao and S. Zhou)
62. "The existence of mild solutions for impulsive fractional partial differential equations", Nonlinear Anal.: TMA, 74 (2011) 2003-2011. (with X.-B. Shu and Y. Lai)
61. "Homoclinic solutions in periodic difference equations with saturable nonlinearity", Sci. China Math., 54 (2011) 83-93. (with Z. Zhou and J. Yu)

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2010

60. "Second-order differentiability with respect to parameters for differential equations with adaptive delays'', Front. Math. China, 5 (2010) 221-286. (with Q. Hu and J. Wu)
59. "On the existence of gap solutions in a periodic discrete nonlinear Schrödinger equation with saturable nonlinearity", Nonlinearity, 23 (2010) 1727-1740. (with Z. Zhou and J. Yu)
58. "Periodic solutions and the global attractor in a system of delay differential equations", SIAM J.  Math.  Anal., 42 (1)(2010) 24-63. (with T. Yi and J. Wu)
57. "Periodic solutions for 2nth-order nonlinear difference equations",  Sci. China Math., 53 (2010) 41-50. (with Z. Zhou and J. Yu)

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2009

56. "Threshold dynamics of a delayed reaction diffusion equation subject to Dirichlet condition", J. Biol. Dyn., 3 (2009) 331-341. (with T. Yi and J. Wu)
55. "Multiple periodic solutions of an impulsive  predator-prey model with Holling-type IV functional response", Math.  Comput.  Modelling, 49 (2009) 1829-1836. (with Q. Wang and B. Dai)

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2008

54. "Complete classification of equilibria and their stability in a delayed neuron network",  Internat. J. Bifur. Chaos Appl. Sci. Engrg., 18 (2008) 2017-2027. (with J. Wu)
53. "Dynamic complexities of a predator-prey model with generalized Holling type III functional response and impulsive effects", Comput. Math. Appl., 56 (2008) 1715-1725. (with H. Su, B. Dai and K. Li)
52. "Permanence and global stability in a discrete $n$-species competition system with feedback controls", Nonlinear Anal. Real World Appl., 9 (4) (2008) 1661-1671. (with X. Liao and S. Zhou)
51.  "Bifurcations in a delayed network: A case study", Journal of Neural Computing Systems, 1 (1) (2008) 39-60. (with S. Guo and J. Wu) 
50. "Stability of the boundary solution of a non-autonomous predator-prey system with the Beddington-DeAngelis functional response", J. Math. Anal. Appl., 344 (2) (2008) 1057-1067.  (with F. Chen and J. Shi)
49. "Two-parameter bifurcations in a network of two neurons with multiple delays", Journal of Differential Equations, 244 (2) (2008) 444-486. (with S. Guo and J. Wu)

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2007

48. "Existence and stability of positive periodic solutions to a periodic integro-differential competition system with infinite delays", International Journal of Qualitative Theory of Differential Equations and Applications, 1 (2) (2007) 124-134. (with F. Chen and S. Guo)
47. "On permanence and global stability in a general Gilpin-Ayala competition predator-prey discrete system", Appl. Math. Comput., 190 (1) (2007) 500-509. (with X. Liao and S. Zhou)
46. "Positive periodic solutions of nonautonomous functional differential systems", J.  Math. Anal. Appl., 333 (2) (2007) 667-678. (with N. Zhang and B. Dai)
45. "Stability and bifurcation of a discrete-time three-neuron system with delays", International Journal of Applied Mathematics and Engineering Sciences, 1 (2007) 89-101. (with S. Guo)
44. "Permanence for a discrete time Lotka-Volterra type food-chain model with delays",  Appl. Math. Comput., 186 (1) (2007) 279-285.  (With X. Liao and S. Zhou)
43. "Network of neurons with delayed feedback: Periodical switching of excitation and inhibition", Dyn. Contin.  Discrete Impuls. Syst. Ser. B: Appl. Algorithms, 14 (1) (2007) 113-122. 

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2006

42. "Linear stability and Hopf bifurcation in a three-unit neural network with two delays",  Neurocomputing, 70 (1-3) (2006) 219-228. (With S. Zou and L. Huang)
41. "Global asymptotic stability of delayed Cohen-Grossberg neural networks", IEEE Trans. Circuits Syst. I Regul. Pap., 53 (2) (2006) 351-357.

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2005

40. "Eventual Periodicity of $$x_n+1=max{1/x_n, A_n/x_n-1} with Periodic Coefficients", J. Difference Equ. Appl.,  11 (15) (2005) 1289-1294.
39. "Existence and global attractivity of a positive periodic solution of a delayed periodic respiration model", Comput. Math. Appl., 49 (5-6) (2005) 677-687. (With L. Huang)
38. "Global attractivity of a circadian pacemaker model in a periodic environment", Discrete and Continuous Dynamical Systems, Series B, 5 (2) (2005) 277-288. (With L. Wang)

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2004

37. "Periodic solutions of a delayed periodic hematopoiesis model", International Journal of Applied Mathematics, 16 (1) (2004) 55-67. (With H. Fang)
36. "New results on positive periodic solutions of a periodic integro-differential competition system", Appl. Math. Comput., 153(2) (2004) 557-565.
35. "Multiple periodic solutions of delayed predator-prey systems with type IV functional responses", Nonlinear Anal. Real World Appl., 5 (1) (2004) 45-53.

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2003

34. "Hopf bifurcation of a positive feedback delay differential equation", Northeast. Math. J., 19 (3) (2003) 213-223. (With L. Huang)
33. "Periodic solution of a delayed periodic logistic equation", Applied Mathematics Letters, 16 (2003) 1047-1051.
32. "Global attractivity and oscillation in a nonlinear periodic delay difference equation", Comput. Math. Appl., 45 (6-9) (2003) 943-950. (With Z. Zhou)
31. "Periodic solutions of delayed predator-prey systems with mutual interference", Differential Equations Dynam. Systems, 11 (3-4) (2003) 321-331.
30. "Global attractivity of a population model with state-dependent delay", Fields Institute Communications, 36 (2003), 113-118.
29. "Stable periodic solution of a discrete periodic Lotka-Volterra competition system", J. Math. Anal. Appl., 277 (2003) 358-366. (With Z. Zhou)
28. "Limiting behavior of a class of delay difference equations", Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 10 (2003) 75-80.
27. "Periodic solutions of delayed periodic Nicholson's blowflies models", Canadian Applied Mathematics Quarterly, 11 (1) (2003), 23-28.

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2002

26. "Unboundedness and periodicity of a system of delay difference equations", Mitt. Math. Sem. Giessen, 248 (2002) 1-19.
25. "All solutions of a class of difference equations are truncated periodic", Appl. Math. Lett. 15 (2002) 975-979.
24. "Boundedness of solutions of a class of nonlinear planar systems", Tohoku Math. J. 54 (2002) no. 3, 393-417. (With L. Huang and J. Wu)
23. "Global stability of neural networks with distributed delays", Neural Networks, 15 (2002) 867-871.
22. "Convergence and periodicity of solutions for a discrete-time network model of two neurons", Math. Comput. Modelling, 35 (2002) 941-950. (With Z. Yuan and L. Huang)

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2001

21. "Special symmetric periodic solutions of delayed monotone feedback systems", Canad. Appl. Math. Quart., 9 (2001) 317-343. (With J. Wu)
20. "Existence and unstable sets of oscillating periodic orbits for delayed excitatory networks of two neurons", Differential Equations Dynam. Systems, 9 (2001) no. 3-4, 169-185.
19. "A remark on 'On stability of nonlinear continuous-time neural networks with delays'", Neural Networks, 14 (2001) 1463.
18. "Existence and attraction of a phase-locked oscillation in a delayed network of two neurons", Differential Integral Equations 14 (2001) 1181-1236. (With J. Wu)
17. "Limiting profiles for periodic solutions of scalar delay differential equations'', Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 799-810.
16. "Slowly oscillating periodic solutions for a delayed frustrated network of two neurons", J. Math. Anal. Appl. 259 (2001) 188-208. (With J. Wu)
15. "A prior bounds and stability of solutions for a Volterra reaction-diffusion equation with infinite delay", Nonlinear Anal., 44 (2001) no. 1, 97-121. (With B. Shi)
14. "Synchronized and nonsymmetric phase-locked periodic solutions in a network of neurons with McCulloch-Pitts nonlinearity", Dynamical Systems and Differential Equations, Proceedings of the International Conference: May 18-21, Kennesaw State University, GA, USA, 102-108.
13. "The asymptotic shapes of periodic solutions of a singular delay differential systems", J. Differential Equations, 169 (2001), 614-632. (With J. Wu)
12. "On real solutions of the equation $$Φ ^t(A)=1/nJ_n", SIAM J. Matrix Anal. Appl. 22 (2001), 965-970.

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2000

11. "Connecting orbits from synchronous periodic solutions to phase-locked periodic solutions in a delay differential system", J. Differential Equations 163 (2000) 130-173. (With J. Wu and T. Krisztin)
10. "Desynchronization of large scale delayed neural networks", Proc. Amer. Math. Soc. 128 (2000) no. 8, 2365-2371. (With Y.-S. Huang and J. Wu)
9. "Periodic solutions of a single species discrete population model with periodic harvest/stock", Comput. Math. Appl. 39 (2000), no. 1-2, 77-90. (With R. Y. Zhang, Z. C. Wang and J. Wu)
8. "Limiting profiles of periodic solutions of neural networks with synaptic delays", Differential equations and computational simulations (Chengdu, 1999), 55-58, World Sci. Publishing, River Edge, NJ, 2000. (with J. Wu)

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1999

7. "Minimal instability and unstable set of a phase-locked orbit in a delayed neural network", Phys. D 134 (1999), no. 2, 185-199. (With J. Wu)
6. "Abstract partial functional differential equations of neutral type: Basic theory", Differential Equations Dynam. Systems, 7 (1999), no. 3, 331-348.

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1996

5. "The linear bi-spatial tensor equation $$φ_ij AⁱXB^j=C", Appl. Math. Mech. (English Ed.) 17 (1996), no. 10, 979-986; translated from Appl. Math. Mech. 17 (1996), no. 10, 919-926 (Chinese). (With H. Xiao and J.-B. Li)
4. "A direct path-preserving algorithm for fuzzy relation equations" (Chinese), Mohu Xitong Yu Shuxue 10 (1996), no. 2, 43-46. (With H.-X. Li)

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1995

3. "The explicit solution of the matrix equation $$AX- XB=C", Appl. Math. Mech. (English Ed.) 16 (1995), no. 12, 1133-1141; translated from Appl. Math. Mech. 16 (1995), no. 12, 1051-1059 (Chinese). (With H. Xiao)
2. "The Hamiltonian structures of 3D ODE with time-independent invariants", Appl. Math. Mech. (English Ed.) 16 (1995), no. 4, 301-306; translated from Appl. Math. Mech. 16 (1995), no. 4, 283-288 (Chinese). (With Z.-H. Guo)

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1994

1. "Intrinsic solution to the $$n-dimensional tensor equation $$∑^m_r=1 U^m-rXU ^r-1=C ", Comput. Methods Appl. Mech. Engrg. 115 (1994), no. 3-4, 359-364. (With Z.-H. Guo, J.-B. Li and H. Xiao)

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