Selected Publications
(The names in italic are Yu's students)
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 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).
 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, 817846, 2017. PDF file
 W. Zhang, L.M. Wahl and P. Yu,
``Backward bifurcations, turning points and rich dynamics
in simple disease models,''
J. Math. Biol., 73(4), 947976, 2016. PDF file
 W. Zhang, L. Wahl and P. Yu,
``Modelling and anlysis of recurrent autoimmune disease,''
SIAM J. Appl. Math., 74(6), 19982025, 2014. PDF file
 W. Zhang, L. Wahl and P. Yu,
``Viral blips may not need a trigger: How transient viremia can arise in
deterministic inhost models,''
SIAM Review, 56(1), 127155, 2014. PDF file ("SIGEST" paper based on the article: SIAM J. Appl. Math., 73(2), 853881, 2013. PDF file)
 P. Yu, M. Han and D. Xiao,
``Four small limit cycles around a Hopf singular point
in 3dimensional competitive LotkaVolterra systems,''
J. Math. Anal. Appl., 436, 521555, 2016. PDF file
 Y. Tian and P. Yu,
``Bifurcation of ten smallamplitude limit cycles by perturbing
a quadratic Hamiltonian system with cubic polynomials,''
J. Diff. Eqns., 260(2), 971990, 2016. PDF file
 Y. Tian and P. Yu,
``Center conditions in a switching Bautin system,''
J. Diff. Equs., 259(3), 12031226, 2015. PDF file
 P. Yu and Y. Tian,
``Twelve limit cycles around a singular point in a planar cubicdegree
polynomial system,''
Commun. Nonl. Sci. Numer. Simulat., 19(8), 26902705, 2014. PDF file
 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
 B. Chan and P. Yu,
``Bifurcation, stability, and cluster formation of multistrain infection
models,''J. Math. Biol., 67(67), 15071532, 2013. PDF file
 B. Chan and P. Yu,
``Bifurcation analysis in a model of cytotoxic Tlymphocyte
response to viralinfection,''
Nonlinear Anal.: Real World Appl., 13, 6477, 2012. PDF file
 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
 M. Gazor and P. Yu,
``Spectral sequences and parametric normal forms,''
J. Diff. Eqns., 252, 10031031, 2012. PDF file
 F. Xu and P. Yu,
``Chaos control and chaos synchronization for multiscroll chaotic
attractors generated using hyperbolic functions,''
J. Math. Anal. Appl, 362(1), 252274, 2010.
PDF file
 P. Yu and R. Corless,
``Symbolic computation of limit cycles associated with Hilbert's 16th
problem,''
Commun. Nonl. Sci. Numer. Simulat., 14(12), 40414056, 2009. PDF file
 P. Yu,
``Computation of limit cycles  the second part of Hilbert's 16th problem,''
The Fields Institute Communications, 49, 151177, 2006. PDF file
 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), 33833390, 2006. PDF file
 Z. Chen and P. Yu,
``DoubleHopf bifurcation in an oscillator with external forcing and
timedelayed feedback controls,''
Int. J. Bifurcation and Chaos, 16(12), 35233537, 2006. PDF file
 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), 606621, 2006. PDF file
 P. Yu,
``Closedform conditions of bifurcation points for general differential
equations,''
Int. J. Bifurcation and Chaos, 15(4), 14671483, 2005. PDF file
 P. Yu and S. Zhu,
``Computation of the normal forms for general MDOF systems using multiple
time scales. Part I: Autonomous systems,''
Commun. Nonl. Sci. Numer. Simulat., 10(8), 869905, 2005. PDF file
 P. Yu and M. Han,
``Twelve limit cycles in a 3rdorder planar system with Z_2 symmetry,''
Commun. Pure Appl. Anal., 3(3), 515526, 2004. PDF file
 W. Yao, C. Essex, P. Yu and M. Davison,
``A measure of predictability,''
Physics Rev. E., 69, 066121: 113, 2004. PDF file
 P. Yu and A.Y.T. Leung,
``The simplest normal form of Hopf bifurcation,''
Nonlinearity, 16(1), 277300, 2003. PDF file
 P. Yu and Y. Yuan,
``A matching pursuit technique for computing the simplest normal forms of
vector fields,''
J. Symbolic Comput., 35(5), 591615, 2003. PDF file
 B. Fraser, P. Yu and T. Lookman,
``Steps towards improving the security of chaotic encryption,''
Physical Rev. E, 66, 017202, 2002. PDF file
 Y. Yuan and P. Yu,
``Computation of simplest normal forms of differential equations
associated with a doublezero eigenvalues,''
Int. J. Bifurcations and Chaos, 11(5), 13071330, 2001. PDF file
 P. Yu,
``Computation of normal forms via a perturbation technique,''
J. Sound Vib., 211(1), 1938, 1998. PDF file
 P. Yu,
``Explicit vibration solutions of a cable under complicated loads,''
ASME J. Appl. Mech., 64(4), 957964, 1997.
PDF file
 P. Yu, Y.M. Desai, A.H. Shah and N. Popplewell,
``Three degreesoffreedom model for galloping, Part I: formulation,''
ASCE J. Engng. Mech., 119(12), 24042425, 1993. PDF file1; ``Three degreesoffreedom model for galloping, Part II: solutions,'' ASCE J. Engng. Mech., 119(12), 24262448, 1993.
PDF file2
 P. Yu and K. Huseyin,
``A perturbation analysis of interactive static and dynamic bifurcations,''
IEEE Trans. Automat. Contr., 33(1), 2841, 1988. PDF file
 P. Yu and K. Huseyin,
``Bifurcations associated with a double zero and a
pair of pure imaginary eigenvalues,''
SIAM J. Appl. Math., 48(2), 229261, 1988. PDF file
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