Selected Publications

(The names in italic are Yu's students)

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  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 (accepted for publication).

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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. PDF file ("SIGEST" paper based on the article: SIAM J. Appl. Math., 73(2), 853-881, 2013. PDF file)

  7. 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

  8. 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

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

  10. 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

  11. 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

  12. 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

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

  14. 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

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

  16. 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

  17. 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

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

  19. 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

  20. 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

  21. 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

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

  23. 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

  24. 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

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

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

  27. 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

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

  29. 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

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

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

  32. 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 file1; ``Three degrees-of-freedom model for galloping, Part II: solutions,'' ASCE J. Engng. Mech., 119(12), 2426-2448, 1993. PDF file2

  33. 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

  34. 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
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