Publications (1986 - 2017)

(Conference proceedings papers and conference presentations not listed)

Back to Yu's home page

  • Monographs
    1. M. Han and P. Yu, Normal Forms, Melnikov Functions, and Bifurcations of limit cycles, Springer-Verlag, New York, 2012.

    2. X. Liao and P. Yu, Absolute Stability of Nonlinear Control Systems, Springer-Verlag, New York, 2008.

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


  • Refereed Journal Papers
      2017

    1. X. Sun and P. Yu, ``Periodic traveling waves in a generalized BBM equation with weak backward diffusion and dissipation terms,'' Discrete Continuous Dyn. Syst. Ser. B (revision under review).

    2. T. Chen, L. Huang, P. Yu and W. Huang, ``Bifurcation of limit cycles at infinity in piecewise polynomial systems,'' Nonlinear Anal. B: Real World Appl. (accepted for publication).

    3. P. Yu, A. Nadeem and L.M. Wahl, ``The impact of prophage on the equilibria and stability of phage and host,'' J. Nonlinear Sci., 27, 817-846, 2017. PDF file

    4. F. Li, P. Yu, Y.R. Liu and Y.Y. Liu, ``Center and isochronous center of a class of quasi-analytic switching systems,'' Sci. China Math. 10.1007/s11425-016-9158-2 (online Aug. 28, 2017).

    5. P. Liu, X. Liu and P. Yu, ``Mixed-mode oscillations in a three-store calcium dynamical model,'' Commun Nonlinear Sci Numer Simulat., 52, 148-164, 2017. PDF file

    6. P. Yu and F. Li, ``Bifurcation of limit cycles in a cubic-order planar system around a nilpotent critical point,'' J. Math. Anal. Appl., 453(2), 645-667, 2017. PDF file

    7. X. Sun, N. Wang and P. Yu, ``The monotonicity of ratios of some Abelian integrals,'' Bull. Sci. Math. (in press) PDF file

    8. J. Jiang and P. Yu, ``Multistable phenomena involving equilibria and periodic motions in predator-prey systems,'' Int. J. Bifurcation and Chaos, 27(3), 1750043 (28 pages), 2017. PDF file

    9. F. Li, Y. Liu and P. Yu, ``Bifurcation of limit cycles at infinity in a class of switching systems,'' Nonlinear Dyn., 88(1), 403-414, 2017. PDF file

    10. J. Yang and P. Yu, ``Nine limit cycles around a nilpotent center in a cubic near-Hamiltonian system,'' Appl. Math. Comput., 298, 141-152, 2017. PDF file


      2016

    11. P. Yu, M. Han and D. Xiao, ``Four small limit cycles around a Hopf singular point in 3-dimensional competitive Lotka-Volterra systems,'' J. Math. Anal. Appl., 436, 521-555, 2016. PDF file

    12. P. Yu and W. Lin, ``Complex dynamics in biological systems arising from multiple limit cycle bifurcation,'' J. Biol. Dyn., 10(1), 263-285, 2016. PDF file

    13. C. Murza and P. Yu, ``Coupled oscillatory systems with D_4 symmetry and application to van der Pol oscillators,'' Int. J. Bifurcation and Chaos, 26(8), 1650141 (18 pages), 2016. PDF file

    14. J. Jiang, Y. Song and P. Yu, ``Delay-induced triple-zero bifurcation in a delayed Leslie-type predator-prey model with additive Allee effect,'' Int. J. Bifurcation and Chaos, 26(7), 1650117, (14 pages), 2016. PDF file

    15. P. Yu, W. Zhang and L.M. Wahl, ``Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence,'' Commun Nonlinear Sci Numer Simulat, 37, 163-192, 2016. PDF file

    16. W. Zhang, L.M. Wahl and P. Yu, ``Backward bifurcations, turning points and rich dynamics in simple disease models,'' J. Math. Biol., 73(4), 947-976, 2016. PDF file

    17. W. Zhang and P. Yu, ``Hopf and generalized Hopf bifurcations in a recurrent autoimmune disease model,'' Int. J. Bifurcation and Chaos, 26(5), 1650079, (24 pages), 2016. PDF file

    18. F. Li, P. Yu and Y. Liu, ``Analytic integrability of two lopsided systems,'' Int. J. Bifurcation and Chaos, 26(2), 1650026, (14 pages), 2016. PDF file

    19. Y. Tian and P. Yu, ``Bifurcation of ten small-amplitude limit cycles by perturbing a quadratic Hamiltonian system with cubic polynomials,'' J. Diff. Eqns., 260(2), 971-990, 2016. PDF file


      2015

    20. 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., 82(1), 131-141, 2015. PDF file

    21. 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 file

    22. Y. Tian and P. Yu, ``Center conditions in a switching Bautin system,'' J. Diff. Equs., 259(3), 1203-1226, 2015. PDF file

    23. 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 file

    24. 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 file


      2014

    25. W. Zhang, L. Wahl and P. Yu, ``Modelling and anlysis of recurrent autoimmune disease,'' SIAM J. Appl. Math., 74(6), 1998-2025, 2014. PDF file

    26. 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 file

    27. 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 file

    28. 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 (10 pages), 2014. PDF file

    29. 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 Review, 56(1), 127-155, 2014. ("SIGEST" paper, a revised version based on the article: SIAM J. Appl. Math., 73(2), 853-881, 2013.) PDF file

    30. 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 file

    31. 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 file

    32. 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 (49 pages), 2014. PDF file


      2013

    33. 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 file

    34. C. Chen, R. Corless, M. Maza, P. Yu and Y. Zhang, ``A modular regular chains method and its application to dynamical systems,'' Int. J. Bifurcation and Chaos, 23(9), 1350154 (21 pages), 2013. PDF file

    35. 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 (33 pages), 2013. PDF file

    36. 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 (18 pages), 2013. PDF file

    37. B. Chan and P. Yu, ``Synchrony-Breaking Hopf Bifurcation in a Model of Antigenic Variation,'' Int. J. Bifurcation and Chaos, 23(2), 1350021 (15 pages), 2013. PDF file

    38. 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 (15 pages), 2013. PDF file

    39. 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 (18 pages), 2013. PDF file

    40. 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 file

    41. M. Han, Y. Tian and P. Yu, ``Small-amplitude limit cycles of polynomial Lienard systems,'' Sci. China Math., 56(8), 1543-1556, 2013. PDF file

    42. 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 file

    43. 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 file

    44. 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 file


      2012

    45. Y. Ding, W. Jiang and P. Yu, ``Hopf-zero bifurcation in a generalized Gopalsamy neural network model,'' Nonlinear Dyn., 70, 1037-1050, 2012. PDF file

    46. P. Yu and M. Han, ``Bifurcation of limit cycles in quadratic Hamiltonian systems with various degree polynomial perturbations,'' Chaos, Solitons and Fractals, 45(6), 772-794, 2012. PDF file

    47. M. Gazor and P. Yu, ``Spectral sequences and parametric normal forms,'' J. Diff. Eqns., 252, 1003-1031, 2012. PDF file

    48. B. Chan and P. Yu, ``Bifurcation analysis in a model of cytotoxic T-lymphocyte response to viralinfection,'' Nonlinear Anal. B: Real World Appl., 13, 64-77, 2012. PDF file

    49. P. Yu and M. Han, ``Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials,'' Int. J. Bifurcation and Chaos, 22(10), 1250254 (28 pages), 2012. PDF file

    50. 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 (21 pages), 2012. PDF file


      2011

    51. P. Yu and J. Lv, ``Bifurcation control for a class of Lorenz-like systems,'' Int. J. Bifurcation and Chaos, 21(9), 2647-2664, 2011. PDF file

    52. P. Yu and M. Han, ``Four limit cycles in quadratic near-integrable system,'' J. Appl. Anal. Comp., 1(2), 291-298, 2011. PDF file

    53. P. Yu and M. Han, ``A study on Zoladek's example,'' J. Appl. Anal. Comp., 1(1), 143-153, 2011. PDF file


      2010

    54. 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 file

    55. M. Gazor and P. Yu, ``Formal decomposition method and parametric normal form,'' Int. J. Bifurcation and Chaos, 20(11), 3487-3415, 2010. PDF file

    56. 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 file

    57. 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 file

    58. 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 file


      2009

    59. 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 file

    60. M. Han, J. Yang and P. Yu, ``Hopf Bifurcations for near-Hamiltonian Systems,'' Int. J. Bifurcation and Chaos, 19(12), 4117-4130, 2009. PDF file

    61. 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 file

    62. 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 file

    63. 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 file

    64. 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 file

    65. 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 file

    66. 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 file


      2008

    67. X. Liao, Y. Fu, S. Xie and P. Yu, ``Globally exponentially attractive sets of the family of Lorenz systems,'' Sci. China F: Information Sci., 51(3), 283-292, 2008. PDF file

    68. Z. Xu, H. Hangan and P. Yu, ``Analytical solutions for invisicid Gaussian impinging jets,'' ASME J. Appl. Mech., 75(2), 021019, 1-12, 2008. PDF file

    69. M. Gazor and P. Yu, ``Infinite order parametric normal form of Hopf singularity,'' Int. J. Bifurcation and Chaos, 18(11), 3393-3408, 2008. PDF file

    70. 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 file

    71. P. Yu and G. Chen, ``Computation of focus values with applications,'' Nonlinear Dyn., 51(3), 409-427, 2008. PDF file

    72. Z. Yan and P. Yu, ``Hyperchaos synchronization and control on a new hyperchaotic attractor,'' Chaos, Solitons & Fractals, 35(2), 333-345, 2008. PDF file

    73. Y. Shi and P. Yu, ``Chaos induced by regular snap-back repellers,'' J. Math. Anal. Appl., 337(2), 1480-1494, 2008. PDF file

    74. H. Chen, Y. Liu and P. Yu, ``Center and isochronous center at infinity in a class of planar systems,'' Dynamics of Continuous, Discrete and Impulsive Systems B: Appl. & Algorithms, 15(1), 57-74, 2008. PDF file

    75. 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 file


      2007

    76. 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 file

    77. 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 file

    78. 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 Information Sci., 37(6), 757-769, 2007. PDF file

    79. P. Yu and R. Chen, ``The simplest parametrized normal forms of Hopf and generalized Hopf bifurcations,'' Nonlinear Dyn., 50(1-2), 297-313, 2007. PDF file

    80. Y. Shi and P. Yu, ``On chaos of the logistic maps,'' Dynamics of Continuous, Discrete and Impulsive Systems B: Appl. & Algorithms, 14(2), 175-195, 2007. PDF file

    81. M. Han, D. Shang, Z. Wang and P. Yu, ``Bifurcation of limit cycles in a 4th-order near-Hamiltonian systems,'' J. Bifurcation and Chaos, 17(11), 4117-4144, 2007. PDF file

    82. 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 file

    83. 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 file

    84. 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 file

    85. 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 file

    86. P. Yu and A. Leung, ``Normal forms of vector fields with perturbation parameters,'' Chaos, Solitons and Fractals, 34(2), 564-579, 2007. PDF file

    87. P. Yu and A. Leung, ``The simplest normal form and its application to bifurcation control,'' Chaos, Solitons and Fractals, 33(3), 845-863, 2007. PDF file

    88. Z. Yan and P. Yu, ``Linear feedback control, adaptive feedback control and their combination for chaos (lag) synchronization of LC chaotic systems,'' Chaos, Solitons and Fractals, 33(2), 419-435, 2007. PDF file

    89. P. Yu and M. Han, ``On limit cycles of the Lienard equations with Z_2 symmetry,'' Chaos, Solitons and Fractals, 33(1), 617-630, 2007. PDF file

    90. W. Yao and P. Yu, ``Bifurcation of small limit cycles in Z_5-equivariant planar vector fields of order 5,'' J. Math. Anal. Appl., 328(1), 400-413, 2007. PDF file


      2006

    91. M. Gazor, P. Yu and H. Gazor, ``Cantor sets in locally compact groups,'' Scientiae Mathematicae Japonicae, 64(3), 525-532, 2006. PDF file

    92. X. Huang, P. Yu and W. Huang, ``Open-loop frequency response for a chaotic system,'' Chinese Physics, 15(12), 2894-2901, 2006. PDF file

    93. Z. Wu and P. Yu, ``A method for stability and bifurcation control,'' IEEE Trans. on Automatic Control, 51(6), 1019-1023, 2006. PDF file

    94. Z. Chen and P. Yu, ``Double-Hopf bifurcation in an oscillator with external forcing and time-delayed feedback controls,'' Int. J. Bifurcation and Chaos, 16(12), 3523-3537, 2006. PDF file

    95. 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 file

    96. 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 file

    97. 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 file

    98. 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 file

    99. 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 file

    100. 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 file

    101. 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 file

    102. 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 file

    103. 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 file

    104. P. Yu and M. Han, ``Limit cycles in generalized Lienard systems,'' Chaos, Solitons and Fractals, 30(5), 1048-1068, 2006. PDF file

    105. S. Wang and P. Yu, ``Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11,'' Chaos, Solitons and Fractals, 30(3), 606-621, 2006. PDF file

    106. X. Liao and P. Yu, ``Chaos control for the family of Rossler systems using feedback controllers,'' Chaos, Solitons and Fractals, 29(1), 91-107, 2006. PDF file

    107. Y. Shi and P. Yu, ``Study on chaos induced by turbulent maps in noncompact sets,'' Chaos, Solitons and Fractals, 28(5), 1165-1180, 2006. PDF file

    108. P. Yu, ``Computation of limit cycles -- the second part of Hilbert's 16th problem,'' The Fields Institute Communications, 49, 151-177, 2006. PDF file

    109. 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 file

    110. 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 file


      2005

    111. 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 file

    112. P. Yu and Z.Q. Wu, ``An exact solution to the stabilization of discrete systems using a first-order controller,'' IEEE Trans. on Automatic Control, 50(9), 1375-1379, 2005. PDF file

    113. 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), 3867-3881, 2005. PDF file

    114. Z. Chen and P. Yu, ``Hopf bifurcation control for an Internet congestion model,'' Int. J. Bifurcation and Chaos, 15(8), 2643-2651, 2005. PDF file

    115. 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 file

    116. P. Yu, ``Closed-form conditions of bifurcation points for general differential equations,'' Int. J. Bifurcation and Chaos, 15(4), 1467-1483, 2005. PDF file

    117. 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 file

    118. S. Wang and P. Yu, ``Bifurcation of limit cycles in a quintic Hamiltonian system under sixth-order perturbation,'' Chaos, Solitons and Fractals, 26(5), 1317-1335, 2005. PDF file

    119. Z. Chen and P. Yu, ``Controlling and anti-controlling Hopf bifurcations in discrete maps using polynomial functions,'' Chaos, Solitons and Fractals, 26(4), 1231-1248, 2005. PDF file

    120. P. Yu and M. Han, ``Small limit cycles from fine focus points in cubic order Z_2-equivariant vector fields,'' Chaos, Solitons and Fractals, 24(1), 329-348, 2005. PDF file

    121. X.F. Chen, P. Yu, M. Han and W. Zhang, ``Canard solutions of 2-D singularly perturbed systems,'' Chaos, Solitons and Fractals, 23(3), 915-927, 2005. PDF file

    122. 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 file


      2004

    123. 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 file

    124. W.H. Chen, Z.H. Guan and P. Yu, ``Delay-dependent stability and H_inifinity control of uncertain discrete-time Markovian jump systems with mode-dependent time delays,'' Syst. Control Lett., 52(5), 361-371, 2004. PDF file

    125. W. Yao, C. Essex, P. Yu and M. Davison, ``A measure of predictability,'' Physics Rev. E., 69, 066121: 1-13, 2004. PDF file

    126. Y. Yuan, P. Yu, L. Librescu and P. Marzocca, ``Aeroelasticity of time-delayed feedback control of two-dimensional supersonic lifting surfaces,'' J. Guidance Control Dyn., 27(5), 795-803, 2004. PDF file

    127. W. Yao, P. Yu and C. Essex, ``Communication between synchronized random number generators,'' Int. J. Bifurcation and Chaos, 14(11), 3995-4008, 2004. PDF file

    128. 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 file

    129. 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 file

    130. 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 file

    131. 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 file

    132. W. Yao, C. Essex, P. Yu and M. Davison, ``Forecast entropy,'' Kebernetes: Int. J. Systems and Cybernetics, 33(5/6), 1009-1015, 2004. PDF file


      2003

    133. P. Yu and A.Y.T. Leung, ``The simplest normal form of Hopf bifurcation,'' Nonlinearity, 16(1), 277-300, 2003. PDF file

    134. P. Yu and Y. Yuan, ``A matching pursuit technique for computing the simplest normal forms of vector fields,'' J. Symbolic Comput., 35(5), 591-615, 2003. PDF file

    135. 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 file

    136. P. Yu and Y. Yuan, ``An efficient method for computing the simplest normal forms of vector fields,'' Int. J. Bifurcations and Chaos, 13(1), 19-46, 2003. PDF file

    137. K. Pan and P. Yu, ``Dynamical analysis on incompressible pre-stressed non-local elastic material'', Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) A: Math. Anal., 10(1), 127-137, 2003. PDF file

    138. P. Yu, ``A simple and efficient method for computing center manifold and normal forms associated with semi-simple cases,'' Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) B: Appl. Algorithms., 10(2), 273-286, 2003. PDF file

    139. A.B. Gumel, S.M. Moghadas, Y. Yuan and P. Yu, ``Bifurcation and stability analysis of a 13-D SEIC model'', Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) B: Appl. Algorithms., 10(2), 317-330, 2003. PDF file

    140. W. Yao, C. Essex and P. Yu, ``A new chaotic system for better secure communication'', Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) B: Appl. Algorithms., 10(2), 221-234, 2003. PDF file

    141. Y. Yuan and P. Yu, ``The simplest normal form for 1:2 double Hopf singularity'', Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) B: Appl. Algorithms., 10(1), 123-136, 2003. PDF file

    142. S. Zhu and P. Yu, ``An algorithm for computing normal forms using perturbation technique'', Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) B: Appl. Algorithms., 10(2), 181-193, 2003. PDF file

    143. P. Yu and K. Pan, ``Direct perturbation analysis on cables with concentrated loads'', Commun. Nonl. Sci. Numer. Simulat., 8(2), 97-112, 2003. PDF file


      2002

    144. P. Yu, ``Analysis on double Hopf bifurcation using computer algebra with the aid of multiple scales,'' Nonlinear Dyn., 27, 19-53, 2002. PDF file

    145. 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 file

    146. B. Fraser, P. Yu and T. Lookman, ``Steps towards improving the security of chaotic encryption,'' Physical Rev. E, 66, 017202, 2002. PDF file

    147. 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 file

    148. 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 file


      2001

    149. 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(4), 597-627, 2001. PDF file

    150. 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 file

    151. P. Yu and A. Gumel, ``Bifurcation and stability analysis for a coupled brusselator model,'' J. Sound & Vib., 244(5), 795-820, 2001. PDF file

    152. P. Yu and Y. Yuan, ``The simplest normal forms associated with a triple zero eigenvalue of indices one and two,'' Nonlinear Anal.: Theory Methods Appl., 47(2), 1105-1116, 2001. PDF file

    153. Y. Yuan and P. Yu, ``Computation of simplest normal forms of differential equations associated with a double-zero eigenvalues,'' Int. J. Bifurcations and Chaos, 11(5), 1307-1330, 2001. PDF file

    154. W. Zhang and P. Yu, ``Degenerate bifurcation analysis on a parametrically and externally excited mechanical system,'' Int. J. Bifurcations and Chaos, 11(3), 689-709, 2001. PDF file

    155. 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 file

    156. W. Yao, P. Yu and C. Essex, ``Delayed stochastic differential model for quiet standing,'' Physical Rev. E, 63, 021902, 2001. PDF file

    157. B. Fraser, P. Yu and T. Lookman, ``Secure communications using chaos synchronization,'' Physics in Canada, 57(2), 155-161, 2001. PDF file

    158. 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,'' Computers Biol. Medicine, 31(5), 287-301, 2001. PDF file

    159. P. Yu and Y. Yuan, ``The simplest normal form for the singularity of a pure imaginary pair and a zero eigenvalue,'' Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) B: Appl. Algorithms., 8, 219-249, 2001. PDF file


      2000

    160. A. Gumel, E. Twizell and P. Yu, ``Numerical and bifurcation analysis for a population model of HIV chemotherapy,'' Math. Computers Simula., 54(1-3), 169-181, 2000. PDF file

    161. 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 file


      1999

    162. Q. Bi and P. Yu, ``Double Hopf bifurcations and chaos of a nonlinear vibration system,'' Nonlinear Dyn., 19(4), 313-332, 1999. PDF file

    163. Q. Bi and P. Yu, ``Symbolic software development for computing the normal forms of double Hopf bifurcation,'' J. Math. Computer Modelling, 29(9), 49-70, 1999. PDF file

    164. Q. Bi and P. Yu, ``Symbolic computation of normal forms for semi-simple cases,'' J. Comput. Appl. Math., 102(2), 195-220, 1999. PDF file

    165. P. Yu, ``Simplest normal forms of Hopf and generalized Hopf bifurcations,'' Int. J. Bifurcation and Chaos, 9(10), 1917-1939, 1999. PDF file


      1998

    166. 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 file

    167. 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 file

    168. 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 file

    169. P. Yu, ``Computation of normal forms via a perturbation technique,'' J. Sound Vib., 211(1), 19-38, 1998. PDF file

    170. 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.in Sci.and Technology, 5, 1998. PDF file


      1997

    171. P. Yu, ``Explicit vibration solutions of a cable under complicated loads,'' ASME J. Appl. Mech., 64(4), 957-964, 1997. PDF file

    172. 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.in Sci.and Technology, 4(2), 93-108; 4(3), 185-196, 1997. PDF file


      1996

    173. 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 file

    174. 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 file

    175. 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 file

    176. Y.M. Desai, P. Yu, A.H. Shah and N. Popplewell, ``Perturbation based finite element analysis of transmission line galloping,'' J. Sound & Vib., 191(4), 469-489, 1996. PDF file


      1995

    177. P. Yu, P.S. Wong and F. Kaempffer, ``Tension of conductor under concentrated loads,'' ASME J. Appl. Mech., 62(3), 802-809, 1995. PDF file

    178. 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 file

    179. Y.M. Desai, P. Yu, N. Popplewell and A.H. Shah, ``Finite element modeling of overhead transmission line galloping,'' Comput. Struct., 57(3), 407-420, 1995. PDF file

    180. 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 file

    181. 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 file


      1993

    182. P. Yu and K. Huseyin, ``On phase-locked motions associated with strong resonance,'' Quarterly Appl. Math., 51(1), 91-100, 1993. PDF file

    183. 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 file

    184. 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 file


      1992

    185. P. Yu, A.H. Shah and Popplewell, ``Inertially coupled galloping of iced conductors,'' ASME J. Appl. Mech., 59(1), 140-145, 1992. PDF file

    186. P. Yu and K. Huseyin, ``Sensitivity analysis of certain dynamic bifurcations,'' Math. & Computer Modelling, 16(10), 45-58, 1992. PDF file


      1991

    187. 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 file


      1990

    188. P. Yu and K. Huseyin, ``On generic dynamics related to a 3-fold zero eigenvalue,'' Dynam. Stabil. Syst., 5(2), 113-126, 1990. PDF file

    189. 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 file


      1989

    190. 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 file

    191. P. Yu and K. Huseyin, ``Invariant tori arising at a general critical point of codimension three,'' Appl. Math. Modelling, 13(9), 506-523, 1989. PDF file


      1988

    192. P. Yu and K. Huseyin, ``A perturbation analysis of interactive static and dynamic bifurcations,'' IEEE Trans. Automat. Contr., 33(1), 28-41, 1988. PDF file

    193. 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 file

    194. P. Yu and K. Huseyin, ``Bifurcations associated with a three-fold zero eigenvalue,'' Quarterly Appl. Math., 46(2), 193-216, 1988. PDF file

    195. K. Huseyin and P. Yu, ``On bifurcations into non-resonant quasi-periodic motions,'' Appl. Math. Modelling, 12(2), 189-201, 1988. PDF file

    196. P. Yu and K. Huseyin, ``Two- and three-dimensional tori bifurcating from interactions of dynamic modes,'' Int. J. Sys. Sci., 19(9), 1763-1780, 1988. PDF file

    197. 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 file


      1986

    198. P. Yu and K. Huseyin, ``Static and dynamic bifurcations associated with a double zero eigenvalue,'' Dynam. Stabil. Syst., 1(1), 73-86, 1986. PDF file
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