PUBLICATIONS (1986-2015)

Back to Yu's home page

  • Monographs  
  • Refereed Journal Papers:   2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001
                                                    1996-2000  1991-1995  1986-1990
  • Refereed Conference Proceedings Papers
  • Chapters in Books  


  • Monographs    (back to top)
    1. M. Han and P. Yu " Normal Forms, Melnikov Functions, and Bifurcations of Limit Cycles," (Springer-Verlag, 2012).

    2. X. Liao and P. Yu " Absolute Stability of Nonlinear Control Systems," (Springer-Verlag, 2008).

    3. X. Liao, L. Wang and P. Yu " Stability of Dynamical Systems," (Elsvier, 2007).

  • Refereed Journal Papers   
    1. 2015   (back to top)

    2. Z. Wei, P. Yu, W. Zhang and M. Yao, " Study of hidden attractors, multiple limit cycles and boundedness of motion in the generalized hyperchaotic Rabinovich system," Nonlinear Dyn. (available online May 21, 2015). (DOI 10.1007/s11071-015-2144-8). [pdf]

    3. F. Li, P. Yu, Y. Tian and Y. Liu, " Center and isochronous center conditions for switching systems associated with elementary singular points," Commun. Nonl. Sci. Numer. Simulat. 28(1-3), 81-97, 2015. [pdf]

    4. Y. Tian and P. Yu, "Center conditions in a switching Bautin system," J. Differential Equations, 259(3), 1203-1226, 2015. [pdf]

    5. P. Yu and M. Han, " Ten limit cycles around a center-type singular point in a 3-d quadratic system with quadratic perturbation," Appl. Math. Lett., 44 (6), 17-20, 2015. [pdf]

    6. X. Chen, L. Huang and P. Yu, "Dynamics behaviour of a class of HIV compartmental models," Commun. Nonl. Sci. Numer. Simulat. 23(1-3), 115-128, 2015. [pdf]

      2014   (back to top)

    7. W. Zhang, L. Wahl and P. Yu, " Modelling and anlysis of recurrent autoimmune disease," SIAM J. Appl. Math., 74(6), 1998-2025, 2014. [pdf]

    8. Y. Tian, Y. Bai and P. Yu, " Impact of delay on HIV-1 dynamics of fighting a virus with another virus," Math. Biosci. Eng., 11(5), 1181-1198, 2014. [pdf]

    9. P. Yu, J. Huang and J. Jiang, " Dynamics of an HIV-1 infection model with cell mediated immunity," Commun. Nonl. Sci. Numer. Simulat., 19(10), 3827-3844, 2014 . [pdf]

    10. Y. Tian and P. Yu, " Seven limit cycles around a focus point in a simple three-dimensional quadratic vector field," Int. J. Bifurcation and Chaos, 24(6), 1450083, 2014 (10 pages). [pdf]

    11. W. Zhang, L. Wahl and P. Yu, "Viral blips may not need a trigger: How transient viremia can arise in deterministic in-host models," SIAM Rev., 56(1), 127-155, 2014. [abstrct.pdf], "Paper" [paper.pdf]

    12. P. Yu and Y. Tian, " Twelve limit cycles around a singular point in a planar cubic-degree polynomial system," Commun. Nonl. Sci. Numer. Simulat., 19(8), 2690-2705, 2014. [pdf]

    13. Y. Tian and P. Yu, " An explicit recursive formula for computing the normal forms associated with semisimple cases," Commun. Nonl. Sci. Numer. Simulat., 19(7), 2294-2308, 2014. [pdf]

    14. P. Yu, Y. Ding and W. Jiang, "Equivalence of MTS method and CMR method for delay differential equations associated with semisimple singularity," Int. J. Bifurcation and Chaos, 24(1), 1450003, 2014 (49 pages). [pdf]

      2013   (back to top)

    15. W. Zhang, L. Wahl and P. Yu, "Conditions for transient viremia in deterministic in-host models: viral blips need no exogenous trigger," SIAM J. Appl. Math., 73(2), 853-881, 2013. [pdf] This paper won A Nugget from SIAM in 2013.

    16. C. Chen, R. Corless, M. Maza, P. Yu and Y. Zhang, "An application of regular chain theory to the study of limit cycles," Int. J. Bifurcation and Chaos, 23(9), 1350154, 2013 (21 pages). [pdf]

    17. F. Xu, P. Yu and X. Liao, "Synchronization and stabilization of multi-scroll integer and fractional order chaotic attractors generated using trigonometric functions," Int. J. Bifurcation and Chaos, 23(8), 1350145, 2013 (33 pages). [pdf]

    18. Y. Tian and P. Yu, "An explicit recursive formula for computing the normal form and center manifold of general n-dimensional differential systems associated with Hopf bifurcation," Int. J. Bifurcation and Chaos, 23(6), 1350104, 2013 (18 pages). [pdf]

    19. B. Chan and P. Yu, "Synchrony-breaking Hopf bifurcation in a model of antigenic variation," Int. J. Bifurcation and Chaos, 23(2), 1350021, 2013 (15 pages). [pdf]

    20. Y. Ding, W. Jiang and P. Yu, "Double Hopf bifurcation in delayed Van der Pol-Duffing equation," Int. J. Bifurcation and Chaos, 23(1), 1350014, 2013 (15 pages). [pdf]

    21. P. Yu and M. Han, "Eight limit cycles around a center in a quadratic Hamiltonian system with third-order perturbation," Int. J. Bifurcation and Chaos, 23(1), 1350005, 2013 (18 pages). [pdf]

    22. Y. Ding, W. Jiang and P. Yu, "Double Hopf bifurcation in a container crane model with delayed position feedback," Appl. Math. Comput., 219(17), 9270-9281, 2013. [pdf]

    23. M. Han, Y. Tian and P. Yu, "Small-amplitude limit cycles of polynomial Lienard systems," Sci. China Math. 56(8), 1543-1556, 2013. [pdf]

    24. Y. Ding, W. Jiang and P. Yu, "Bifurcation analysis in a recurrent neural network model with delays," Commun. Nonl. Sci. Numer. Simulat., 18(2), 351-372, 2013. [pdf]

    25. P. Yu and M. Han, "Bifurcation of limit cycles in 3rd-order Z_2 Hamiltonian planar vector fields with 3rd-order perturbations," Commun. Nonl. Sci. Numer. Simulat., 18(4), 978-988, 2013. [pdf]

    26. B. Chan and P. Yu, "Bifurcation, stability, and cluster formation of multi-strain infection models," J. Math. Biol., 67(6-7), 1507-1532, 2013. [pdf]

      2012   (back to top)

    27. Y. Ding, W. Jiang and P. Yu, "Hopf-zero bifurcation in a generalized Gopalsamy neural network model," Nonlinear Dyn., 70(2), 1037-1050, 2012. [pdf]

    28. P. Yu and M. Han, "Bifurcation of limit cycles in quadratic Hamiltonian systems with various degree polynomial perturbations," Chaos Solitons Fractals, 45(6), 772-794, 2012. [pdf]

    29. M. Gazor and P. Yu, "Spectral sequences and parametric normal forms," J. Differential Equations, 252(2), 1003-1031, 2012. [pdf]

    30. B. Chan and P. Yu, "Bifurcation analysis in a model of cytotoxic T-lymphocyte response to viralinfection," Nonlinear Anal. Real World Appl., 13(1), 64-77, 2012. [pdf]

    31. P. Yu and M. Han, "Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials," Int. J. Bifurcation and Chaos, 22(10), 1250254, 2012 (28 pages). [pdf]

    32. P. Yu and X. Zou, "Bifurcation analysis on an HIV-1 Model with constant injection of recombinant," Int. J. Bifurcation and Chaos, 22(3), 1250062, 2012 (21 pages). [pdf]

      2011   (back to top)

    33. P. Yu and J. Lu, "Bifurcation control for a class of Lorenz-like systems," Int. J. Bifurcation and Chaos, 21(9), 2647-2664, 2011. [pdf]

    34. P. Yu and M. Han, "Four limit cycles in quaratic near-integrable system," J. Appl. Anal. Comput., 1(2), 291-298, 2011. [pdf]

    35. P. Yu and M. Han, "A study on Zoladek's example," J. Appl. Anal. Comput., 1(1), 143-153, 2011. [pdf]

      2010   (back to top)

    36. P. Yu, M. Han and J. Li, "Bifurcation of limit cycles in cubic integrable Z_2-equivariant planar vector fields," Qual. Theory Dyn. Syst., 9(1-2), 221-233, 2010. [pdf]

    37. M. Gazor and P. Yu, "Formal decomposition method and parametric normal form," Int. J. Bifurcation and Chaos, 20(11), 3487-3415, 2010. [pdf]

    38. J. Yang, M. Han, J. Li and P. Yu, "Existence conditions of thirteen limit cycles in a cubic system," Int. J. Bifurcation and Chaos, 20(8), 2569-2577, 2010. [pdf]

    39. P. Yu, M. Han and J. Zhang, "Critical periods of 3rd-order planar Hamiltonian systems," Int. J. Bifurcation and Chaos, 20(7), 2213-2224, 2010. [pdf]

    40. F. Xu and P. Yu, "Chaos control and chaos synchronization for multi-scroll chaotic attractors generated using hyperbolic functions," J. Math. Anal. Appl, 362(1), 252-274, 2010. [pdf]

      2009   (back to top)

    41. X. Jiang, P. Yu, Z. Yuan and X. Zou, "Dynamics of a HIV-1 therapy model of fighting a virus with another virus," J. Biol. Dyn., 3(4), 387-409, 2009. [pdf]

    42. M. Han, J. Yang and P. Yu, "Hopf Bifurcations for near-Hamiltonian Systems," Int. J. Bifurcation and Chaos, 19(12), 4117-4130, 2009. [pdf]

    43. F. Xu and P. Yu, "Global stabilization and synchronization of n-scroll-chaotic attractors in a modified Chua's circuit with hyperbolic tangent function," Int. J. Bifurcation and Chaos, 19(8), 2563-2572, 2009. [pdf]

    44. P. Yu and M. Han, "Critical periods of planar revertible vector field with 3rd-degree polynomial functions," Int. J. Bifurcation and Chaos, 19(1), 419-433, 2009. [pdf]

    45. F. Xu, P. Yu and X. Liao, "Global analysis on n-scroll-chaotic attractors of modified Chua's circuit," Int. J. Bifurcation and Chaos, 19(1), 135-157, 2009. [pdf]

    46. P. Yu and R. Corless, "Symbolic computation of limit cycles associated with Hilbert's 16th problem," Commun. Nonl. Sci. Numer. Simulat., 14(12), 4041-4056, 2009. [pdf]

    47. P. Yu, X. Liao, S. Xie and Y. Fu, "A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family," Commun. Nonl. Sci. Numer. Simulat., 14(7), 2886-2896, 2009. [pdf]

    48. X. Liao, F. Xu, P. Wang and P. Yu, "Chaos control and synchronization for a special generalized Lorenz canonical system -- the SM system," Chaos Solitons Fractals, 39(5), 2491-2508, 2009. [pdf]

      2008   (back to top)

    49. X. Liao, Y. Fu, S. Xie and P. Yu, "Globally exponentially attractive sets of the family of Lorenz systems," Sci. China Inf. Sci., 51(3), 283-292, 2008. [pdf]

    50. Z. Xu, H. Hangan and P. Yu, "Analytical solutions for a family of Gaussian impinging jets," ASME J. Appl. Mech., 75(2), 021019, 1-12, 2008. [pdf]

    51. M. Gazor and P. Yu, "Infinite order parametric normal form of Hopf singularity," Int. J. Bifurcation and Chaos, 18(11), 3393-3408, 2008. [pdf]

    52. Z. Zeng, P. Yu and X. Liao, "A new comparison method for stability theory of differential systems with time-varying delays," Int. J. Bifurcation and Chaos, 18(1), 169-186, 2008. [pdf]

    53. P. Yu and G. Chen, "Computation of focus values with applications," Nonlinear Dyn., 51(3), 409-427, 2008. [pdf]

    54. Z. Yan and P. Yu, "Hyperchaos synchronization and control on a new hyperchaotic attrator," Chaos Solitons Fractals, 35(2), 333-345, 2008. [pdf]

    55. Y. Shi and P. Yu, "Chaos induced by regular snap-back repellers," J. Math. Anal. Appl., 337(2), 1480-1494, 2008. [pdf]

    56. H. Chen, Y. Liu and P. Yu, "Center and isochronous center at infinity in a class of planar systems," Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 15(1), 57-73, 2008. [pdf]

    57. P. Yu and X. Liao, "On the study of globally exponentially attractive set of a general chaotic system," Commun. Nonl. Sci. Numer. Simulat., 13(8), 1495-1507, 2008. [pdf]

      2007   (back to top)

    58. X. Liao, Z. Chen, F. Xu and P. Yu, "Robust absolute stability of Lurie interval control systems," Int. J. Robust Nonlinear Control, 17, 1669-1689, 2007 [pdf]

    59. P. Yu, Z. Chen, L. Librescu and P. Marzocca "Implications of time-delayed feedback control on limit cycle oscillation of a 2-dimensional supersonic lifting surfaces," J. Sound Vib., 304(3-5), 974-986, 2007. [pdf]

    60. X. Liao, H. Luo, Y. Fu, S. Xie and P. Yu, "Analysis on the global exponential set and positive invariant set of the Lorenz family," Sci. China Inf. Sci., 37(6), 757-769, 2007. [pdf]

    61. P. Yu and G. Chen, "The simplest parametrized normal forms of Hopf and generalized Hopf bifurcations," Nonlinear Dyn., 50(1-2), 297-313, 2007. [pdf]

    62. Y. Shi and P. Yu, "On chaos of the logistic maps," Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 14(2), 175-195, 2007. [pdf]

    63. M. Han, D. Shang, Z. Wang and P. Yu, "Bifurcation of limit cycles in a 4th-order near-Hamiltonian system," Int. J. Bifurcation and Chaos, 17(11), 4117-4144, 2007. [pdf]

    64. P. Yu, W. Yao and G. Chen, "Analysis on topological properties of the Lorenz and the Chen attractors using GCM," Int. J. Bifurcation and Chaos, 17(8), 2791-2796, 2007. [pdf]

    65. J. Jiang, M. Han, P. Yu and S. Lynch, "Limit cycles in two types of symmetric Lienard systems," Int. J. Bifurcation and Chaos, 17(6), 2169-2174, 2007. [pdf]

    66. Z. Yan and P. Yu, "Globally exponential hyperchaos (lag) synchronization in a family of modified hyperchaotic Rossler systems," Int. J. Bifurcation and Chaos, 17(5), 1759-1774, 2007. [pdf]

    67. P. Yu, "Local and global bifurcations to limit cycles in a class of Lienard equation," Int. J. Bifurcation and Chaos, 17(1), 183-198, 2007. [pdf]

    68. P. Yu and A. Leung, "Normal forms of vector fields with perturbation parameters and their application," Chaos Solitons Fractals 34(2), 564-579, 2007. [pdf]

    69. P. Yu and A. Leung, "The simplest normal form and its application to bifurcation control," Chaos Solitons Fractals 33(3), 845-863, 2007. [pdf]

    70. Z. Yan and P. Yu, "Linear feedback control, adaptive feedback control and their combination for chaos (lag) synchronization of LC chaotic systems," Chaos Solitons Fractals, 33(2), 419-435, 2007. [pdf]

    71. P. Yu and M. Han, "On limit cycles of the Lienard equations with Z_2 symmetry," Chaos Solitons Fractals, 31(3), 617-630, 2007. [pdf]

    72. W. Yao and P. Yu, "Bifurcation of small limit chycles in Z_5-equivariant planar vector fields of order 5," J. Math. Anal. Appl., 328(1), 400-413, 2007. [pdf]

      2006   (back to top)

    73. M. Gazor and P. Yu and H. Gazor, "Cantor sets in locally compact groups," Scientiae Mathematicae Japonicae, 64(3), 525-532, 2006. [pdf]

    74. X. Huang, P. Yu and W. Huang, "Open-loop frequency response for a chaotic system," Chinese Physics, 15(12), 2894-2901, 2006. [pdf]

    75. Z. Wu and P. Yu, "A method for stability and bifurcation control," IEEE Trans. Autom. Control, 51 (9), 1019-1023, 2006. [pdf]

    76. Z. Chen and P. Yu, "Double-Hopf bifurcation in an oscillator with external forcing and time-delayed feedback control," Int. J. Bifurcation and Chaos, 16(12), 3523-3537, 2006. [pdf]

    77. P. Yu and F. Xu, "A common phenomenon in chaotic systems linked by time delay," Int. J. Bifurcation and Chaos, 16(12), 3727-3736, 2006. [pdf]

    78. P. Yu and X. Liao, "New estimations for globally attractive and positive invariant set of the family of the Lorenz systems," Int. J. Bifurcation and Chaos, 16(11), 3383-3390, 2006. [pdf]

    79. X. Liao, P. Yu, S. Xie and Y. Fu, "Study on the global property of the smooth Chua's system," Int. J. Bifurcation and Chaos, 16(10), 2815-2841, 2006. [pdf]

    80. Y. Shi, P. Yu and G. Chen, "Chaotification of discrete dynamical systems in Banach spaces," Int. J. Bifurcation and Chaos, 16(9), 2615-2636, 2006. [pdf]

    81. X. Liao and P. Yu, "Study of globally exponential synchronization for the family of Rossler systems," Int. J. Bifurcation and Chaos, 16(8), 2395-2406, 2006. [pdf]

    82. S. Wang, P. Yu and J. Li, "Bifurcation of limit cycles in a Z_10-equivariant vector fields of degree 9," Int. J. Bifurcation and Chaos, 16(8), 2309-2324, 2006. [pdf]

    83. P. Yu and X. Liao, "Globally attractive and positive invariant set of the Lorenz system," Int. J. Bifurcation and Chaos, 16(3), 757-764, 2006. [pdf]

    84. W. Yao, P. Yu, C. Essex and M. Davison, "Competitive modes and their application," Int. J. Bifurcation and Chaos, 16(3), 497-522, 2006. [pdf]

    85. S. Zhu and P. Yu, "Computation of the normal forms for general M-DOF systems using multiple time scales. Part II: Non-autonomous systems," Commun. Nonl. Sci. Numer. Simulat., 11(1), 45-81, 2006. [pdf]

    86. P. Yu and M. Han, "Limit cycles in generalized Lienard systems," Chaos Solitons Fractals, 30(5), 1048-1068, 2006. [pdf]

    87. S. Wang and P. Yu, "Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11," Chaos Solitons Fractals, 30(3), 606-621, 2006. [pdf]

    88. X. Liao and P. Yu, "Chaos control for the family of Rossler systems using feedback controllers," Chaos Solitons Fractals, 29(1), 91-107, 2006. [pdf]

    89. Y. Shi and P. Yu, "Study on Chaos induced by turbulent maps in noncompact sets," Chaos Solitons Fractals, 28(5), 1165-1180, 2006. [pdf]

    90. P. Yu, "Computation of limit cycles -- the second part of Hilbert's 16th problem," Fields Inst. Commun., 49, 151-177, 2006. [pdf]

    91. X. Liao and P. Yu, "Sufficient and necessary conditions for the absolute stability of time-delayed Lurie control systems," J. Math. Anal. Appl., 323(2), 876-890, 2006. [pdf]

    92. P. Yu, M. Han and Y. Yuan, "Analysis on limit cycles of Z_q-equivariant polynomial vector fields with degree 3 or 4," J. Math. Anal. Appl., 322(1), 51-65, 2006. [pdf]

      2005   (back to top)

    93. S.R. Valluri, P. Yu, G.R. Smith and P. Wiegert, "The Apsidal angle and its derivative in Newton's apsidal precession theorem," Mon. Not. R. Astron. Soc., 358, 1273-1284, 2005. [pdf]

    94. P. Yu and Z. Wu, "An exact solution to the stabilization of discrete systems using a first-order controller," IEEE Trans. Autom. Control, 50 (9), 1375-1379, 2005. [pdf]

    95. X. Liao and P. Yu, "Analysis on the global exponent synchronization of Chua's circuit using absolute stability theory," Int. J. Bifurcation and Chaos, 15(12), 3687-3881, 2005. [pdf]

    96. Z. Chen and P. Yu, "Hopf bifurcation control for an internet congestion model," Int. J. Bifurcation and Chaos, 15(8), 2643-2651, 2005. [pdf]

    97. P. Yu and M. Han, "Twelve limit cycles in a cubic case of the 16th Hilbert problem," Int. J. Bifurcation and Chaos, 15(7), 2191-2205, 2005. [pdf]

    98. P. Yu, "Closed-form conditions of bifurcation points for general differential equations," Int. J. Bifurcation and Chaos, 15(4), 1467-1483, 2005. [pdf]

    99. Z. Chen, Z. Wu and P. Yu, "Modelling of the critical phenomena due to the interaction between hysteretic damping and external force," J. Sound Vib., 284(3-5), 783-803, 2005. [pdf]

    100. S. Wang and P. Yu, "Bifurcation of limit cycles in a quintic Hamiltonian system under sixth-order perturbation," Chaos Solitons Fractals, 26(5), 1317-1335, 2005. [pdf]

    101. Z. Chen and P. Yu, "Controlling and anti-controlling Hopf bifurcations in discrete maps using polynomial functions," Chaos Solitons Fractals, 26(4), 1231-1248, 2005. [pdf]

    102. P. Yu and M. Han, "Small limit cycles bifurcating from fine focus points in cubic order Z_2-equivariant vector fields," Chaos Solitons Fractals, 24(1), 329-348, 2005. [pdf]

    103. X.F. Chen, P. Yu, M. Han and W.J. Zhang, "Canard solutions of two-dimentional singularly perturbed systems," Chaos Solitons Fractals, 23(3), 915-927, 2005. [pdf]

    104. P. Yu and S. Zhu, "Computation of the normal forms for general M-DOF systems using multiple time scales. Part I: Autonomous systems," Commun. Nonl. Sci. Numer. Simulat., 10(8), 869-905, 2005. [pdf]

      2004   (back to top)

    105. P. Yu and M. Han, "Twelve limit cycles in a 3rd-order planar system with Z_2 symmetry," Commun. Pure Appl. Anal., 3(3), 515-526, 2004. [pdf]

    106. W.-H. Chen, Z.-H. Guan and P. Yu, "Delay-dependent stability and H_infinity control of uncertain discrete-time Markovian jump systems with mode-dependent time delays," Systems & Control Letters, 52(5), 361-371, 2004. [pdf]

    107. W. Yao, C. Essex, P. Yu and M. Davison, "Measure of predictability," Phys. Rev. E, 69, 066121: 1-13, 2004. [pdf]

    108. Y. Yuan, P. Yu, L. Librescu and P. Marzocca, "Aeroelasticity of time-delayed feedback control of two-dimensional supersonic lifting surfaces," J. Guidance, Control, and Dynamics, 27(5), 795-803, 2004. [pdf]

    109. W. Yao, P. Yu and C. Essex, "Communication between synchronized random number generators," Int. J. Bifurcation and Chaos, 14(11), 3995-4008, 2004. [pdf]

    110. J. Xu and P. Yu, "Delay-induced bifurcations in a non-autonomous system with delayed velocity feedbacks," Int. J. Bifurcation and Chaos, 14(8), 2777-2798, 2004. [pdf]

    111. Z. Wu, P. Yu and K. Wang, "Bifurcation analysis on a self-excited hysteretic system," Int. J. Bifurcation and Chaos, 14(8), 2825-2842, 2004. [pdf]

    112. P. Yu and G. Chen, "Hopf bifurcation control using nonlinear feedback with polynomial functions," Int. J. Bifurcation and Chaos, 14(5), 1683-1704, 2004. [pdf]

    113. M. Han Y. Lin and P. Yu, "A study on the existence of limit cycles of a planar system with 3rd-degree polynomials," Int. J. Bifurcation and Chaos, 14(1), 41-60, 2004. [pdf]

    114. W. Yao, C. Essex, P. Yu and M. Davison, "Forecast entropy," Kybernetes: Int. J. Systems and Cybernetics, 33(5/6), 1009-1015, 2004. [pdf]

      2003   (back to top)

    115. P. Yu and A.Y.T. Leung, "The simplest normal form of Hopf bifurcation," Nonlinearity, 16(1), 277-300, 2003. [pdf]

    116. P. Yu and Y. Yuan, "A matching pursuit technique for computing the simplest normal forms of vector fields," J. Symb. Comput., 35(5), 591-615, 2003. [pdf]

    117. P. Yu and A.Y.T. Leung, "A perturbation method for computing the simplest normal forms of dynamical systems," J. Sound Vib., 261(1), 123-151, 2003. [pdf]

    118. P. Yu and Y. Yuan, "An efficient method for computing the simplest normal forms of vector fields," Int. J. Bifurcation and Chaos, 13(1), 19-46, 2003. [pdf]

    119. K. Pan and P. Yu, "Dynamical analysis on incompressible pre-stressed non-local elastic material," Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 10(1), 127-137, 2003. [pdf]

    120. P. Yu, "A simple and efficient method for computing center manifold and normal forms associated with semi-simple cases," Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 10(2), 273-286, 2003. [pdf]

    121. A.B. Gumel, S.M. Moghadas, Y. Yuan and P. Yu, "Bifurcation and stability analysis of a 13-D SEIC model," Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 10(2), 317-330, 2003. [pdf]

    122. W. Yao, C. Essex and P. Yu, "A new chaotic system for better secure communication," Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 10(2), 221-234, 2003. [pdf]

    123. Y. Yuan and P. Yu, "The simplest normal form for 1:2 double Hopf singularity," Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 10(1), 123-136, 2003. [pdf]

    124. S. Zhu and P. Yu, "An algorithm for computing normal forms using perturbation technique," Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 10(2), 181-193, 2003. [pdf]

    125. P. Yu and K. Pan, "Direct perturbation analysis on cables with concentrated loads," Commun. Nonl. Sci. Numer. Simulat., 8(2), 97-112, 2003. [pdf]

      2002   (back to top)

    126. P. Yu, "Analysis on double Hopf bifurcation using computer algebra with the aid of multiple scales," Nonlinear Dyn., 27, 19-53, 2002. [pdf]

    127. P. Yu, "Computation of the simplest normal forms with perturbation parameters based on Lie transform and rescaling," J. Comput. Appl. Math., 144(1-2), 359-373, 2002. [pdf]

    128. B. Fraser, P. Yu and T. Lookman, "Steps towards improving the security of chaotic encryption," Phys. Rev. E, 66, 017202, 2002. [pdf]

    129. W. Yao, P. Yu and C. Essex, "Estimation of chaotic parameter regimes via generalized competitive mode approach," Commun. Nonl. Sci. Numer. Simulat., 7(4), 197-205, 2002. [pdf]

    130. P. Yu, Y. Yuan and J. Xu, "Study of double Hopf bifurcation and chaos for an oscillator with time delayed feedback," Commun. Nonl. Sci. Numer. Simulat., 7(1-2), 69-91, 2002. [pdf]

      2001   (back to top)

    131. P. Yu, W. Zhang and Q. Bi, "Vibration analysis on a thin plate with the aid of computation of normal forms," Int. J. Non-Linear Mech., 36, 597-627, 2001. [pdf]

    132. P. Yu, "Symbolic computation of normal forms for resonant double Hopf bifurcations using multiple time scales," J. Sound Vib., 247(4), 615-632, 2001. [pdf]

    133. P. Yu and A. Gumel, "Bifurcation and stability analysis for a coupled brusselator model," J. Sound Vib., 244(5), 795-820, 2001. [pdf]

    134. P. Yu and Y. Yuan, "The simplest normal forms associated with a triple zero eigenvalue of indices one and two," Nonlinear Anal., 47(2), 1105-1116, 2001. [pdf]

    135. Y. Yuan and P. Yu, "Computation of simplest normal forms of differential equations associated with a double-zero eigenvalues," Int. J. Bifurcation and Chaos, 11(5), 1307-1330, 2001. [pdf]

    136. W. Zhang and P. Yu, "Degenerate bifurcation analysis on a parametrically and externally excited mechanical system," Int. J. Bifurcation and Chaos, 11(3), 689-709, 2001. [pdf]

    137. W. Zhang, Z. Liu and P. Yu, "Global dynamics of a parametrically and externally excited thin plate," Nonlinear Dyn., 24(3), 245-268, 2001. [pdf]

    138. W. Yao, P. Yu and C. Essex, "Delayed stochastic differential model for quiet standing," Phys. Rev. E, 63, 021902 (8 pages), 2001. [pdf]

    139. B. Fraser, P. Yu and T. Lookman, "Secure communications using chaos synchronization," Physics in Canada, Special Issue on Nonlinear Dynamics, 57(2), 155-161, 2001. [pdf]

    140. A. Gumel, T.D. Loewen, P.N. Shivakumar, B.M. Sahai, P. Yu and M.L. Garba, "Numerical modelling of the perturbation of HIV-1 during combination anti-retroviral therapy," Comput. Biol. Med., 31(5), 287-301, 2001. [pdf]

    141. P. Yu and Y. Yuan, "The simplest normal form for the singularity of a pure imaginary pair and a zero eigenvalue," Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 8b(2), 219-249, 2001. [pdf]

      1996-2000   (back to top)

    142. A. Gumel, E. Twizell and P. Yu, "Numerical and bifurcation analysis for a population model of HIV chemotherapy," Math. Comput. Simulat., 54(1-3), 169-181, 2000. [pdf]

    143. W. Zhang and P. Yu, "A Study of the limit cycles associated with a generalized codimension-3 Lienard oscillator," J. Sound Vib., 231(1), 145-173, 2000. [pdf]


    144. P. Yu, "Simplest normal forms of Hopf and generalized Hopf bifurcations," Int. J. Bifurcation and Chaos , 9(10), 1917-1939, 1999. [pdf]

    145. Q. Bi and P. Yu, "Double Hopf bifurcations and chaos of a nonlinear vibration system," Nonlinear Dyn., 19, 313-332, 1999. [pdf]

    146. Q. Bi and P. Yu, "Symbolic software development for computing the normal forms of double Hopf bifurcation," Math. Comput. Model., 29(9), 49-70, 1999. [pdf]

    147. Q. Bi and P. Yu, "Symbolic computation of normal forms for semi-simple cases," J. Comput. Appl. Math., 102, 195-220, 1999. [pdf]


    148. P. Yu, "Computation of normal forms via a perturbation technique," J. Sound Vib., 211(1), 19-38, 1998. [pdf]

    149. P. Yu and K. Huseyin, "Parametrically excited nonlinear systems: A comparison of certain methods," Int. J. Non-Linear Mech., 33(6), 967-978, 1998. [pdf]

    150. P. Yu and K. Huseyin, Bifurcation and stability analysis of nonlinear systems via the intrinsic harmonic balancing technique, Part II: non-autonomous systems, J. Nonlinear Dyn. Sci. Tech., 5, 1998. [pdf]

    151. P. Yu and Q. Bi, "Analysis of non-linear dynamics and bifurcations of a double pendulum," J. Sound Vib., 217(4), 691-736, 1998. [pdf]

    152. Q. Bi and P. Yu, "Computation of normal forms of differential equations associated with non-semisimple zero eigenvalues," Int. J. Bifurcation and Chaos, 8(12), 2279-2319, 1998. [pdf]


    153. P. Yu and K. Huseyin, Bifurcation and stability analysis of nonlinear systems via the intrinsic harmonic balancing technique, Part I: autonomous systems, J. Nonlinear Dyn. Sci. Tech., 4(2), 93-108, 1997; 4(3), 185-196, 1997. [pdf]

    154. P. Yu, "Explicit vibration solutions of a cable under complicated loads," ASME J. Appl. Mech., 64, 957-964, 1997. [pdf]


    155. P. Yu, Y.M. Desai, N. Popplewell and A.H. Shah, "The Krylov-Bogoliubov and Galerkin methods for nonlinear oscillations," J. Sound Vib., 192(2), 413-438, 1996. [pdf]

    156. P. Yu, U. Taneri and K. Huseyin, "Forced Oscillations, bifurcations and stability of a molecular system (Part I): non-resonance," Int. J. Sys. Sci., 27(12), 1339-1350, 1996. [pdf]

    157. P. Yu, U. Taneri and K. Huseyin, "Forced Oscillations, bifurcations and stability of a molecular system (Part II): resonances," Int. J. Sys. Sci., 27(12), 1351-1361, 1996. [pdf]

    158. Y.M. Desai, P. Yu, A.H. Shah and N. Popplewell, "Perturbation based finite element analysis of transmission line galloping," J. Sound Vib., vol. 191(4), 469-489, 1996. [pdf]

      1991-1995   (back to top)

    159. P. Yu, P.S. Wong and F. Kaempffer, "Tension of conductor under concentrated loads," ASME J. Appl. Mech., 62, 802-809, 1995. [pdf]

    160. U. Taneri, K. Huseyin and P. Yu, "Analysis of bifurcations and stability properties of molecular systems," Dynam. Stabil. Syst., 10(2), 149-162, 1995. [pdf]

    161. Y.M. Desai, P. Yu, N. Popplewell and A.H. Shah, "Finite element modeling of overhead transmission line galloping," J. Comput. Struct., 57(3), 407-420, 1995. [pdf]

    162. P. Yu, N. Popplewell and A.H. Shah, "Instability trends of inertially coupled galloping, Part I: initiation," J. Sound Vib., 183(4), 663-678, 1995. [pdf]

    163. P. Yu, N. Popplewell and A.H. Shah, "Instability trends of inertially coupled galloping, Part II: periodic vibrations," J. Sound Vib., 183(4), 679-691, 1995. [pdf]


    164. P. Yu, Y.M. Desai, A.H. Shah and N. Popplewell, "Three degrees-of-freedom model for galloping, Part I: formulation," ASCE J. Engng. Mech., 119(12), 2404-2425, 1993. [pdf]

    165. P. Yu, Y.M. Desai, N. Popplewell and A.H. Shah, "Three degrees-of-freedom model for galloping, Part II: solutions," ASCE J. Engng. Mech., 119(12), 2426-2448, 1993. [pdf]

    166. P. Yu and K. Huseyin, "On phase-locked motions associated with strong resonance," Quart. Appl. Math., 51(1), 91-100, 1993. [pdf]


    167. P. Yu, A.H. Shah and Popplewell, "Inertially coupled galloping of iced conductors," ASME J. Appl. Mech., 59, 140-145, 1992. [pdf]

    168. P. Yu and K. Huseyin, "Sensitivity analysis of certain dynamic bifurcations," J. Math. Comput. Model., 16(10), 45-58, 1992. [pdf]


    169. P. Yu, N. Popplewell and A.H. Shah, "A geometrical approach assessing instability trends for galloping," ASME J. Appl. Mech., 58, 784-791, 1991. [pdf]

      1986-1990   (back to top)

    170. P. Yu and K. Huseyin, "On generic dynamics related to a 3-fold zero eigenvalue," Dynam. Stabil. Syst., 5(2), 113-126, 1990. [pdf]

    171. P. Yu and K. Huseyin, "Dynamic behavior of an autonomous system with three pairs of pure imaginary eigenvalues," Int. J. Sys. Sci., 21(6), 993-1024, 1990. [pdf]


    172. K. Huseyin and P. Yu, "On the dynamics and stability of a codimension-3 autonomous system," Int. J. Engng. Sci., 27(5), 583-604, 1989. [pdf]

    173. P. Yu and K. Huseyin, "Invariant tori arising at a general critical point of codimension three," Appl. Math. Model., 13, 506-523, 1989. [pdf]


    174. P. Yu and K. Huseyin, "A perturbation analysis of interactive static and dynamic bifurcations," IEEE Trans. Autom. Control, 33(1), 28-41, 1988. [pdf]

    175. P. Yu and K. Huseyin, "Bifurcations associated with a double zero and a pair of pure imaginary eigenvalues," SIAM J. Appl. Math., 48(2), 229-261, 1988. [pdf]

    176. P. Yu and K. Huseyin, "Bifurcations associated with a triple-zero eigenvalue of index two or three," ZAMM Z. Angew. Math. Mech., 68(4), T142-T145, 1988. [pdf]

    177. P. Yu and K. Huseyin, "Bifurcations associated with a three-fold zero eigenvalue," Quart. Appl. Math., 46(2), 193-216, 1988. [pdf]

    178. K. Huseyin and P. Yu, "On bifurcations into non-resonant quasi-periodic motions," Appl. Math. Model., 12, 189-201, 1988. [pdf]

    179. P. Yu and K. Huseyin, "2- and 3-D tori bifurcating from the interaction of static and dynamic modes," Int. J. Sys. Sci., 19(9), 1763-1780, 1988. [pdf]

    180. P. Yu and K. Huseyin, "Bifurcations associated with a double zero of index two and a pair of pure imaginary eigenvalues," Int. J. Sys. Sci., 19(1), 1-21, 1988. [pdf]


    181. P. Yu and K. Huseyin, "Static and dynamic bifurcations associated with a double zero eigenvalue," Dynam. Stabil. Syst., 1(1), 73-86, 1986. [pdf]



  • Refereed Conference Proceedings Papers     (back to top)
    1. X. Liao, F. Xu and P. Yu, "Absolute stability of Hopfield neural network," Advances in Neural Networks (ISNN 2006) (May 28-June 1, 2006, Chengdu, China), Proc. Part I. Lecture Notes in Computer Science, 3971, 249-254, 2006. [pdf]

    2. Z. Chen, P. Yu, P. Marzocca and L. Librescu, "Time-delayed feedback control of a 2-D supersonic flapped wings," 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (May 1-4, 2006, Hyatt Regency Newport, Newport, Rhode Island), DOI: 10.2514/6.2006-1835 [pdf]

    3. S. Zhu, P. Yu and S. Jones, "An efficient computation method for Hopf bifurcation of high dimensional systems," Pooc. of IDECT'05, ASME Int. Mech. Eng. Cong. Exp. (Sept. 24-28, 2005, Long Beach, CA), DETC2005-84835, 689-694. [pdf]

    4. Z. Chen and P. Yu, "Double-Hopf bifurcation in an oscillator with external forcing and time-delayed feedback control," Pooc. of IDECT'05, ASME Int. Mech. Eng. Cong. Exp. (Sept. 24-28, 2005, Long Beach, CA), DETC2005-85549, 715-723. [pdf]

    5. P. Yu and Z. Chen, L. Librescu and P. Marzocca, "Stability, bifurcation and jumping phenomenon in a 2-D model of supersonic lifting surfaces," Pooc. of IDECT'05, ASME Int. Mech. Eng. Cong. Exp. (Sept. 24-28, 2005, Long Beach, CA), DETC2005-85549, 695-703. [pdf]

    6. X. Liao and P. Yu, "Chaos control and synchronization for the family of Rossler systems," Proc. of DCDIS 4th Int. Conf. on Engineering Applications and Computational Algorithms (July 27-29, 2005, Guelph), 433-438. [pdf]

    7. Y. Shi and P. Yu, "Chaos induced by snap-back eepellers and its applications to anti-control of chaos," Proc. of DCDIS 4th Int. Conf. on Engineering Applications and Computational Algorithms (July 27-29, 2005, Guelph), 364-369. [pdf]

    8. Z. Chen and P. Yu, "Parametric study on the stability of a 2-D supersonic lifting surface with time delayed linear and nonlinear feedback controls," Proc. of DCDIS 4th Int. Conf. on Engineering Applications and Computational Algorithms (July 27-29, 2005, Guelph), 535-540. [pdf]

    9. P. Yu and F. Xu, "A study on chaotic systems with time delay," Proc. of DCDIS 4th Int. Conf. on Engineering Applications and Computational Algorithms (July 27-29, 2005, Guelph), 754--758. [pdf]

    10. P. Yu, Z. Chen, L. Librescu and P. Marzocca, "Implications of time delayed feedback control on LCO of supersonic lifting surfaces," 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (April 18-21, 2005, Austin, Texas), AIAA-2005-2375, 6954-6971. [pdf]

    11. Y. Shi, P. Yu and G. Chen, "Anti-control of discrete chaos in Banach spaces," Proc. of the 5th EUROMECH Nonlinear Dynamics Conference (August 7-12, 2005, the Eindhoven University of Technology, The Netherlands) 1191-1199. [pdf]

    12. P. Yu, Y. Yuan, L. Librescu and P. Marzocca, "Single/double Hopf bifurcation and aeroelastic instability of a 2-D supersonic lifting surface with time delayed feedback control," 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (April 19-22, 2004, Palm Springs, CA), AIAA-2005-1752, 2634-2653. [pdf]

    13. Z. Chen, Z. Wu and P. Yu, "Analysis on critical phenomena of a hysteretic system," Proc. of 2003 ASME Int. Mech. Eng. Cong. Exp. (Nov. 15-21, 2003, Washington, D.C.), IMECE2003-55000, 725-731. [pdf]

    14. Z. Wu and P. Yu, "Bifurcation control of Rossler system," Proc. of 2003 ASME Int. Mech. Eng. Cong. Exp. (Nov. 15-21, 2003, Washington, D.C.), IMECE2003-55035, 733-740. [pdf]

    15. P. Yu, "Computation of the normal form for 1:1 resonant double Hopf bifurcation," Proc. of DCDIS 3rd Int. Conf. on Engineering Applications and Computational Algorithms (May 15-18, 2003, Guelph), 121-126. [pdf]

    16. P. Yu and Y. Yuan, "The simplest normal form of generalized Hopf bifurcation with perturbation parameters," Proc. of DCDIS 3rd Int. Conf. on Engineering Applications and Computational Algorithms (May 15-18, 2003, Guelph), 127-132. [pdf]

    17. S. Zhu and P. Yu, "A comparison of perturbation methods," Proc. of DCDIS 3rd Int. Conf. on Engineering Applications and Computational Algorithms (May 15-18, 2003, Guelph), 402-407. [pdf]

    18. P. Yu, "A general formula for controlling Hopf bifurcation," Proc. of 2002 ASME Int. Mech. Eng. Cong. Exp. (Nov. 17-22, 2002, New Orleans), IMECE2002-32397, 333-340. [pdf]

    19. K. Pan and P. Yu, "Direct perturbation analysis on transmission lines with detuning pendulums," Vibration and Control of Mechanical Systems. (ASME, Nov. 11-16, 2001, New York), DE-Vol. 111, 255-264. [pdf]

    20. W. Yao, P. Yu and C. Essex, "Estimation of chaotic parameter regimes via generalized competitive modes approach," Vibration and Control of Mechanical Systems. (ASME, Nov. 11-16, 2001, New York), DE-Vol. 111, 193-198. [pdf]

    21. P. Yu and Y. Yuan, "Analysis on an osicillator with delayed feedback near double Hopf bifurcation," Vibration and Control of Mechanical Systems. (ASME, Nov. 11-16, 2001, New York), DE-Vol. 111, 117-128. [pdf]

    22. P. Yu, "A method for computing center manifold and normal forms," Int. Conf. on Differential Equations (August 1-7, 1999, Berlin), 2, 832-837, World Scientific, Singapore, 2000. [pdf]

    23. N. Popplewell, A.H. Shah, P. Yu, Y. M. Desai and P. Stumpf, "Galloping of iced electrical transmission lines," Proc. of 7th Int. Workshop on Atmospheric Icing of Structures (June 3-7, 1996, Universite du Quebec a Chicoutini, Quebec), 291-294. [pdf]

    24. P. Yu and Y. Yuan, "Simplest normal form of a codimension-two system," Proc. of 17th CANCAM (May 30-June 3, 1999, Hamilton), 367-368. [pdf]

    25. P. Yu and Z. Zhao, "Direct perturbation analysis on nonlinear cable vibrations," Proc. of 17th CANCAM (May 30-June 3, 1999, Hamilton), 109-110. [pdf]

    26. S. Zhu and P. Yu, "Computing normal forms for vibration analysis of nonlinear oscillators via multiple time scales," Proc. of 17th CANCAM (May 30-June 3, 1999, Hamilton), 69-70. [pdf]

    27. P. Yu and K. Huseyin, "On the analysis of internal non-resonant double Hopf bifurcation with symbolic software," Proc. of 15th CANCAM (May 28-June 1, 1995, Victoria), 2, 830-831. [pdf]

    28. P. Yu, N. Popplewell and A.H. Shah, "Free vibration analysis of sagged cables under distributed and concentrated loads," Proc. of 15th CANCAM (May 28-June 1, 1995, Victoria), 1, 374-375. [pdf]

    29. P. Yu, Y.M. Desai, P. Stumpf, N. Popplewell and A.H. Shan, "Galloping of a single electrical transmission line," Proc. of 12th Symp. on Engng. Appl. Mech. (EAM) (1994, Montreal), 7-12, 1994.

    30. P. Yu, Y.M. Desai and N. Popplewell, "Predicting the galloping of an electrical transmission line," Proc. of 13th CANCAM (June 2-6, 1991, Winnipeg), 2, 522-523.

    31. C.Y. Ip, Y.M. Desai, P. Yu, A.H. Shah and N. Popplewell, "An oscillator model for the galloping of an electrical transmission line," Proc. of 4th Int. Conf. on Recent Advances in Structural Dynamics (July 15-18, 1991, Southeampton, U.K.), 801-810, 1991.

    32. P. Yu and K. Hyseyin, "Stability and bifurcation analysis on a generic codimension-3 system," Proc. of 9th Symp. on Engng. Appl. Mech. (EAM), 96-103, 1988.

    33. P. Yu and K. Huseyin, "A codimension-3 bifurcation problem and its application to electrical circuits," Proc. of IEEE Int. Symp. on Circuits Syst. (ISCAS), (June 7-9, 1988, Helsinki), 1, 255-259, 1988. [pdf]

    34. P. Yu and K. Huseyin, "Bifurcations associated with a double zero general critical point," Proc. of 11th CANCAM (May 31-June 4, 1987, University of Alberta, Edmonton), 1, A-156-157. [pdf]

    35. K. Huseyin and P. Yu, "Bifurcations associated with a simple zero and two pairs of pure imaginary eigevalues," Proc. of CMS Annual Seminar: Oscillation, Bifurcation and Chaos (July 13-25, 1986, Toronto), 8, 465-484, 1987 (Eds. F.V. Atkinson, S.F. Langford and A.B.M. Mingarelli). [pdf]



  • Chapters in Books    (back to top)
    1. P. Yu " Bifurcation, Limit Cycle and Chaos of Nonlinear Dynamical Systems," in Bifurcation and Chaos in Complex Systems (Eds. J. Sun and A. Luo), Vol. 1, pp. 1-125, Elsevier: New York, 2006. [pdf]

    2. P. Yu " Bifurcation Dynamics in Control Systems," in Bifurcation Control: Theory and Applications (Eds. G. Chen, D.J. Hill and X. Yu), pp. 99-126, Springer-Verlag: New York, 2003. [pdf]


    Back to Publication List


    URL: http://pyu1.apmaths.uwo.ca/~pyu
    Revised: Feb. 10, 2003