
Mathematical Biology
 P. Liu, X. Liu and P. Yu,
``Mixedmode oscillations in a threestore calcium dynamical model,''
Commun Nonlinear Sci Numer Simulat., 52, 148164, 2017.
PDF file
 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
 J. Jiang and P. Yu,
``Multistable phenomena involving equilibria and periodic
motions in predatorprey systems,''
Int. J. Bifurcation and Chaos, 27(3), 1750043 (28 pages), 2017. 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
 P. Yu and W. Lin,
``Complex dynamics in biological systems arising from
multiple limit cycle bifurcation,''
J. Biol. Dyn., 10(1), 263285, 2016. PDF file
 J. Jiang, Y. Song and P. Yu,
``Delayinduced triplezero bifurcation in a delayed Leslietype
predatorprey model with additive Allee effect,''
Int. J. Bifurcation and Chaos, 26(7), 1650117,
(14 pages), 2016. PDF file
 P. Yu, W. Zhang and L.M. Wahl,
``Dynamical analysis and simulation of a 2dimensional disease model
with convex incidence,''
Commun Nonlinear Sci Numer Simulat, 37, 163192, 2016. 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 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
 X. Chen, L. Huang and P. Yu,
``Dynamics behaviour of a class of HIV compartmental models,''
Commun. Nonl. Sci. Numer. Simulat., 23(13),
115128, 2015. 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
 Y. Tian, Y. Bai and P. Yu,
``Impact of delay on HIV1 dynamics of fighting a virus with another virus,''
Math. Biosci. Eng., 11(5), 11811198, 2014. PDF file
 P. Yu, J. Huang and J. Jiang,
``Dynamics of an HIV1 infection model with cell mediated immunity,''
Commun. Nonl. Sci. Numer. Simulat., 19(10), 38273844, 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. ("SIGEST" paper, a revised version based on the article: SIAM J. Appl. Math., 73(2), 853881, 2013.) PDF file
 W. Zhang, L. Wahl and P. Yu,
``Conditions for transient viremia in deterministic inhost models:
viral blips need no exogenous trigger,''
SIAM J. Appl. Math., 73(2), 853881, 2013.
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 X. Zou,
``Bifurcation analysis on an HIV1 Model with constant
injection of recombinant,''
Int. J. Bifurcation and Chaos, 22(3), 1250062 (21 pages), 2012. PDF file
 X. Jiang, P. Yu, Z. Yuan and X. Zou,
``Dynamics of a HIV1 therapy model of fighting a virus with another virus,''
J. Biol. Dyn., 3(4), 387409, 2009.
PDF file
 M. Han, J. Yang and P. Yu,
``Hopf Bifurcations for nearHamiltonian Systems,''
Int. J. Bifurcation and Chaos, 19(12), 41174130, 2009. PDF file
 A.B. Gumel, S.M. Moghadas, Y. Yuan and P. Yu,
``Bifurcation and stability analysis of a 13D SEIC model'',
Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) B: Appl. Algorithms., 10(2), 317330, 2003. PDF file
 A. Gumel, T.D. Loewen, P.N. Shivakumar, B.M. Sahai, P. Yu
and M.L. Garba,
``Numerical modelling of the perturbation of HIV1 during combination
antiretroviral therapy,''
Computers Biol. Medicine, 31(5), 287301, 2001. PDF file
 A. Gumel, E. Twizell and P. Yu,
``Numerical and bifurcation analysis for a population model of
HIV chemotherapy,''
Math. Computers Simula., 54(13), 169181, 2000. PDF file

Travelling Wave
 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).
 X. Sun, P. Yu and B. Qin,
``Global existence and uniqueness of periodic waves in a
population model with densitydependent migrations and Allee effect,''
Int. J. Bifurcation and Chaos (accepted for publication)

Hilbert's 16th Problem and Limit Cycles Theory
 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).
 P. Yu and F. Li,
``Bifurcation of limit cycles in a cubicorder planar system
around a nilpotent critical point,''
J. Math. Anal. Appl., 453(2), 645667, 2017. PDF file
 X. Sun, N. Wang and P. Yu,
``The monotonicity of ratios of some Abelian integrals,''
Bull. Sci. Math. (in press) PDF file
 J. Yang and P. Yu,
``Nine limit cycles around a nilpotent center in a cubic
nearHamiltonian system,''
Appl. Math. Comput., 298, 141152, 2017. 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
 P. Yu and M. Han,
``Ten limit cycles around a centertype singular point
in a 3d quadratic system with quadratic perturbation,''
Appl. Math. Lett., 44(6), 1720, 2015. PDF file
 Y. Tian and P. Yu,
``Seven limit cycles around a focus point in a simple threedimensional
quadratic vector field,''
Int. J. Bifurcation and Chaos, 24(6), 1450083
(10 pages), 2014. 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
 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
 P. Yu and M. Han,
``Eight limit cycles around a center in a quadratic Hamiltonian system
with thirdorder perturbation,''
Int. J. Bifurcation and Chaos, 23(1), 1350005 (18 pages), 2013. PDF file
 M. Han, Y. Tian and P. Yu,
``Smallamplitude limit cycles of polynomial Lienard systems,''
Sci. China Math., 56(8), 15431556, 2013. PDF file
 P. Yu and M. Han, ``Bifurcation of limit cycles in 3rdorder Z_2
Hamiltonian planar vector fields with 3rdorder perturbations,''
Commun. Nonl. Sci. Numer. Simulat., 18(4), 978988, 2013. PDF file
 P. Yu and M. Han,
``Bifurcation of limit cycles in quadratic Hamiltonian
systems with various degree polynomial perturbations,''
Chaos, Solitons and Fractals, 45(6), 772794, 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
 P. Yu and M. Han,
``Four limit cycles in quadratic nearintegrable system,''
J. Appl. Anal. Comp., 1(2), 291298, 2011. PDF file
 P. Yu and M. Han,
``A study on Zoladek's example,''
J. Appl. Anal. Comp., 1(1), 143153, 2011. PDF file
 P. Yu, M. Han and J. Li,
``Bifurcation of limit cycles in cubic integrable Z_2equivariant planar
vector fields,''
Qual. Theory Dyn. Syst., 9(12), 221233, 2010. PDF file
 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), 25692577, 2010. PDF file
 P. Yu, M. Han and J. Zhang,
``Critical periods of 3rdorder planar Hamiltonian systems,''
Int. J. Bifurcation and Chaos, 20(7), 22132224, 2010. PDF file
 P. Yu and M. Han,
``Critical periods of planar revertible vector field with 3rddegree
polynomial functions,''
Int. J. Bifurcation and Chaos, 19(1), 419433, 2009. 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>
 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), 5774, 2008. PDF file
 M. Han, D. Shang, Z. Wang and P. Yu,
``Bifurcation of limit cycles in a 4thorder nearHamiltonian systems,''
J. Bifurcation and Chaos, 17(11), 41174144, 2007. PDF file
 J. Jiang, M. Han, P. Yu and S. Lynch,
``Limit cycles in two types of symmetric Li\'{e}nard systems,''
Int. J. Bifurcation and Chaos, 17(6), 21692174, 2007. PDF file
 P. Yu,
``Local and global bifurcations to limit cycles in a class of Lienard
equation,''
Int. J. Bifurcation and Chaos, 17(1), 183198, 2007. PDF file
 P. Yu and M. Han,
``On limit cycles of the Lienard equations with Z_2 symmetry,''
Chaos, Solitons and Fractals, 33(1), 617630, 2007. PDF file
 W. Yao and P. Yu,
``Bifurcation of small limit cycles in Z_5equivariant planar vector
fields of order 5,''
J. Math. Anal. Appl., 328(1), 400413, 2007. PDF file
 S. Wang, P. Yu and J. Li,
``Bifurcation of limit cycles in a Z_10equivariant vector fields of
degree 9,''
Int. J. Bifurcation and Chaos, 16(8), 23092324, 2006. PDF file
 P. Yu and M. Han,
``Limit cycles in generalized Lienard systems,''
Chaos, Solitons and Fractals, 30(5), 10481068, 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,
``Computation of limit cycles  the second part of Hilbert's 16th problem,''
The Fields Institute Communications, 49, 151177, 2006. PDF file
 P. Yu, M. Han and Y. Yuan,
``Analysis on limit cycles of Z_qequivariant polynomial vector
fields with degree 3 or 4,''
J. Math. Anal. Appl., 322(1), 5165, 2006. PDF file
 P. Yu and M. Han,
``Twelve limit cycles in a cubic case of the 16th Hilbert problem,''
Int. J. Bifurcation and Chaos, 15(7), 21912205, 2005. PDF file
 S. Wang and P. Yu,
``Bifurcation of limit cycles in a quintic Hamiltonian system
under sixthorder perturbation,''
Chaos, Solitons and Fractals, 26(5), 13171335, 2005. PDF file
 P. Yu and M. Han,
``Small limit cycles from fine focus points in cubic order
Z_2equivariant vector fields,''
Chaos, Solitons and Fractals, 24(1), 329348, 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
 M. Han, Y. Lin and P. Yu,
``A study on the existence of limit cycles of a planar system with 3rddegree
polynomials'',
Int. J. Bifurcation and Chaos, 14(1), 4160, 2004. PDF file
 W. Zhang and P. Yu,
``A Study of the limit cycles associated with a generalized codimension3
Lienard oscillator,''
J. Sound & Vib., 231(1), 145173, 2000. PDF file

Nonlinear Dynamics and Chaos
 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
 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), 131141, 2015. PDF file
 F. Xu, P. Yu and X. Liao,
``Synchronization and stabilization of multiscroll integer and fractional
order chaotic attractors generated using trigonometric functions,''
Int. J. Bifurcation and Chaos, 23(8), 1350145 (33 pages), 2013. PDF file
 P. Yu and J. Lv,
``Bifurcation control for a class of Lorenzlike systems,''
Int. J. Bifurcation and Chaos, 21(9), 26472664, 2011. 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
 F. Xu and P. Yu,
``Global stabilization and synchronization of
nscrollchaotic attractors in a modified Chua's circuit with hyperbolic
tangent function,''
Int. J. Bifurcation and Chaos, 19(8), 25632572, 2009. PDF file
 F. Xu, P. Yu and X. Liao,
``Global analysis on nscrollchaotic attractors of modified Chua's circuit,''
Int. J. Bifurcation and Chaos, 19(1), 135157, 2009. PDF file
 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), 28862896, 2009. PDF file
 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), 24912508, 2009. PDF file
 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), 283292, 2008. PDF file
 Z. Yan and P. Yu,
``Hyperchaos synchronization and control on a new hyperchaotic attractor,''
Chaos, Solitons & Fractals, 35(2), 333345, 2008. PDF file
 Y. Shi and P. Yu,
``Chaos induced by regular snapback repellers,''
J. Math. Anal. Appl., 337(2), 14801494, 2008. PDF file
 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), 14951507, 2008. PDF file
 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), 757769, 2007. PDF file
 Y. Shi and P. Yu,
``On chaos of the logistic maps,''
Dynamics of Continuous, Discrete and Impulsive Systems B: Appl. & Algorithms, 14(2), 175195, 2007. PDF file
 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), 27912796, 2007. PDF file
 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), 17591774, 2007. PDF file
 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), 419435, 2007. PDF file
 M. Gazor, P. Yu and H. Gazor,
``Cantor sets in locally compact groups,''
Scientiae Mathematicae Japonicae, 64(3), 525532, 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
 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), 28152841, 2006. PDF file
 Y. Shi, P. Yu and G. Chen,
``Chaotification of discrete dynamical systems in Banach spaces,''
Int. J. Bifurcation and Chaos, 16(9), 26152636, 2006. PDF file
 X. Liao and P. Yu,
``Study of globally exponential synchronization for the family of Rossler
systems,''
Int. J. Bifurcation and Chaos, 16(8), 23952406, 2006. PDF file
 P. Yu and X. Liao,
``Globally attractive and positive invariant set of the Lorenz system,''
Int. J. Bifurcation and Chaos, 16(3), 757764, 2006. PDF file
 W. Yao, P. Yu, C. Essex and M. Davison,
``Competitive modes and their application'',
Int. J. Bifurcation and Chaos, 16(3), 497522, 2006. PDF file
 X. Liao and P. Yu,
``Chaos control for the family of Rossler systems using feedback
controllers,''
Chaos, Solitons and Fractals, 29(1), 91107, 2006. PDF file
 Y. Shi and P. Yu,
``Study on chaos induced by turbulent maps in noncompact sets,''
Chaos, Solitons and Fractals, 28(5), 11651180, 2006. PDF file
 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), 38673881, 2005. PDF file
 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), 221234, 2003. PDF file
 W. Yao, P. Yu and C. Essex,
``Estimation of chaotic parameter regimes via generalized competitive
mode approach,''
Commun. Nonl. Sci. Numer. Simulat., 7(4), 197205, 2002. PDF file
 Q. Bi and P. Yu,
``Double Hopf bifurcations and chaos of a nonlinear vibration system,''
Nonlinear Dyn., 19(4), 313332, 1999. PDF file

Stability and Bifurcation
 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
 B. Chan and P. Yu,
``SynchronyBreaking Hopf Bifurcation in a Model of Antigenic Variation,''
Int. J. Bifurcation and Chaos, 23(2), 1350021 (15 pages), 2013. PDF file
 Z. Zeng, P. Yu and X. Liao,
``A new comparison method for stability theory of differential systems
with timevarying delays,''
Int. J. Bifurcation and Chaos, 18(1), 169186, 2008. PDF file
 X. Liao, Z. Chen, F. Xu and P. Yu,
``Robust absolute stability of Lurie interval control systems,''
Int. J. Robust & Nonlinear Control, 17, 16691689, 2007. PDF file
 Z. Wu and P. Yu,
``A method for stability and bifurcation control,''
IEEE Trans. on Automatic Control, 51(6), 10191023, 2006. PDF file
 X. Liao and P. Yu,
``Sufficient and necessary conditions for the absolute stability
of timedelayed Lurie control systems,''
J. Math. Anal. Appl., 323(2), 876890, 2006. PDF file
 P. Yu and Z.Q. Wu,
``An exact solution to the stabilization of discrete
systems using a firstorder controller,''
IEEE Trans. on Automatic Control, 50(9), 13751379, 2005. PDF file
 Z. Chen and P. Yu,
``Hopf bifurcation control for an Internet congestion model,''
Int. J. Bifurcation and Chaos, 15(8), 26432651, 2005. PDF file
 P. Yu,
``Closedform conditions of bifurcation points for general differential
equations,''
Int. J. Bifurcation and Chaos, 15(4), 14671483, 2005. PDF file
 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(35), 783803, 2005. PDF file
 Z. Chen and P. Yu,
``Controlling and anticontrolling Hopf bifurcations in discrete maps
using polynomial functions,''
Chaos, Solitons and Fractals, 26(4), 12311248, 2005. PDF file
 X.F. Chen, P. Yu, M. Han and W. Zhang,
``Canard solutions of 2D singularly perturbed systems,''
Chaos, Solitons and Fractals, 23(3), 915927, 2005. PDF file
 Z. Wu, P. Yu and K. Wang,
``Bifurcation analysis on a selfexcited hysteretic system'',
Int. J. Bifurcation and Chaos, 14(8), 28252842, 2004. PDF file
 P. Yu and G. Chen,
``Hopf bifurcation control using nonlinear feedback with polynomial
functions'',
Int. J. Bifurcation and Chaos, 14(5), 16831704, 2004. PDF file
 P. Yu and A. Gumel,
``Bifurcation and stability analysis for a coupled brusselator model,''
J. Sound & Vib., 244(5), 795820, 2001. PDF file
 W. Zhang and P. Yu,
``Degenerate bifurcation analysis on a parametrically and externally
excited mechanical system,''
Int. J. Bifurcations and Chaos, 11(3), 689709, 2001. PDF file
 W. Zhang, Z. Liu and P. Yu,
``Global dynamics of a parametrically and externally excited thin plate,''
Nonlinear Dyn., 24(3), 245268, 2001. PDF file
 P. Yu and Q. Bi,
``Analysis of nonlinear dynamics and bifurcations of a double pendulum,''
J. Sound Vib., 217(4), 691736, 1998. PDF file
 P. Yu and K. Huseyin,
``Parametrically excited nonlinear systems: A comparison of certain methods,''
Int. J. NonLinear Mech., 33(6), 967978, 1998.
PDF file
 P. Yu and K. Huseyin,
``Bifurcation and stability analysis of nonlinear
systems via the intrinsic harmonic balancing technique;
Part II: nonautonomous systems,''
J. Nonlinear Dyn.in Sci.and Technology, 5, 1998. PDF file
 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), 93108; 4(3), 185196, 1997. PDF file
 P. Yu, U. Taneri and K. Huseyin,
``Forced Oscillations, bifurcations and stability of a molecular
system (Part I): nonresonance,''
Int. J. Sys. Sci., 27(12), 13391350, 1996. PDF file
 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), 13511361, 1996. PDF file
 U. Taneri, K. Huseyin and P. Yu,
``Analysis of bifurcations and stability properties of molecular systems,''
Dynam. & Stabil. Syst., 10(2), 149162, 1995. PDF file
 P. Yu and K. Huseyin,
``On phaselocked motions associated with strong resonance,''
Quarterly Appl. Math., 51(1), 91100, 1993. PDF file

Nonsmooth Dynamical Systems
 F. Li, P. Yu, Y.R. Liu and Y.Y. Liu,
``Center and isochronous center of a class of
quasianalytic switching systems,''
Sci. China Math. 10.1007/s1142501691582 (online Aug. 28, 2017).
 F. Li, Y. Liu and P. Yu,
``Bifurcation of limit cycles at infinity in a class of switching systems,''
Nonlinear Dyn., 88(1), 403414, 2017. PDF file
 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(13), 8197,
2015. PDF file
 Y. Tian and P. Yu,
``Center conditions in a switching Bautin system,''
J. Diff. Equs., 259(3), 12031226, 2015. PDF file

Delay Differential Systems
 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
 Y. Ding, W. Jiang and P. Yu,
``Double Hopf bifurcation in delayed Van der PolDuffing equation,''
Int. J. Bifurcation and Chaos, 23(1), 1350014 (15 pages), 2013. PDF file
 Y. Ding, W. Jiang and P. Yu,
``Double Hopf bifurcation in a container crane model with delayed position
feedback,''Appl. Math. Comput., 219(17), 92709281, 2013. PDF file
 Y. Ding, W. Jiang and P. Yu,
``Bifurcation analysis in a recurrent neural network model with delays,''
Commun. Nonl. Sci. Numer. Simulat., 18(2),
351372, 2013. PDF file
 Y. Ding, W. Jiang and P. Yu,
``Hopfzero bifurcation in a generalized Gopalsamy neural network model,''
Nonlinear Dyn., 70, 10371050, 2012. PDF file
 P. Yu, Z. Chen, L. Librescu and P. Marzocca,
``Implications of timedelayed feedback control on limit cycle oscillation
of a 2dimensional supersonic lifting surfaces,''
J. Sound & Vib., 304(35), 974986, 2007. 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
 P. Yu and F. Xu,
``A common phenomenon in chaotic systems linked by time delay,''
Int. J. Bifurcation and Chaos, 16(12), 37273736, 2006. PDF file
 W.H. Chen, Z.H. Guan and P. Yu,
``Delaydependent stability and H_inifinity control of
uncertain discretetime Markovian jump systems with modedependent
time delays,''
Syst. Control Lett., 52(5), 361371, 2004. PDF file
 Y. Yuan, P. Yu, L. Librescu and P. Marzocca,
``Aeroelasticity of timedelayed feedback control of twodimensional
supersonic lifting surfaces,''
J. Guidance Control Dyn., 27(5), 795803, 2004. PDF file
 J. Xu and P. Yu,
``Delayinduced bifurcations in a nonautonomous system with delayed velocity
feedbacks,''
Int. J. Bifurcation and Chaos, 14(8), 27772798, 2004. PDF file
 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(12), 6991, 2002. PDF file
 W. Yao, P. Yu and C. Essex,
``Delayed stochastic differential model for quiet standing,''
Physical Rev. E, 63, 021902, 2001. PDF file

The Simplest Normal Forms
 M. Gazor and P. Yu,
``Spectral sequences and parametric normal forms,''
J. Diff. Eqns., 252, 10031031, 2012. PDF file
 M. Gazor and P. Yu,
``Formal decomposition method and parametric normal form,''
Int. J. Bifurcation and Chaos, 20(11), 34873415, 2010. PDF file
 M. Gazor and P. Yu,
``Infinite order parametric normal form of Hopf singularity,''
Int. J. Bifurcation and Chaos, 18(11), 33933408, 2008. PDF file
 P. Yu and R. Chen,
``The simplest parametrized normal forms of Hopf and generalized Hopf
bifurcations,''
Nonlinear Dyn., 50(12), 297313, 2007. PDF file
 P. Yu and A. Leung,
``The simplest normal form and its application to bifurcation control,''
Chaos, Solitons and Fractals, 33(3), 845863, 2007. 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
 P. Yu and A.Y.T. Leung,
``A perturbation method for computing the simplest normal forms of dynamical
systems,''
J. Sound & Vib., 261(1), 123151, 2003. PDF file
 P. Yu and Y. Yuan,
``An efficient method for computing the simplest normal forms of vector
fields,''
Int. J. Bifurcations and Chaos, 13(1), 1946, 2003. PDF file
 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), 123136, 2003. PDF file
 P. Yu,
``Computation of the simplest normal forms with perturbation parameters
based on Lie transform and rescaling,''
J. Comput. Appl. Math., 144(12), 359373, 2002. PDF file
 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), 11051116, 2001. 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 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, 219249, 2001. PDF file
 P. Yu,
``Simplest normal forms of Hopf and generalized Hopf bifurcations,''
Int. J. Bifurcation and Chaos, 9(10), 19171939, 1999. PDF file

Conventional Normal Forms
 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), 22942308,
2014. PDF file
 Y. Tian and P. Yu,
``An explicit recursive formula for computing the normal form and center
manifold of general ndimensional differential systems associated with
Hopf bifurcation,''
Int. J. Bifurcation and Chaos, 23(6), 1350104 (18 pages), 2013. PDF file
 P. Yu and G. Chen,
``Computation of focus values with applications,''
Nonlinear Dyn., 51(3), 409427, 2008. PDF file
 P. Yu and A. Leung,
``Normal forms of vector fields with perturbation parameters,''
Chaos, Solitons and Fractals, 34(2), 564579, 2007. PDF file
 S. Zhu and P. Yu,
``Computation of the normal forms for general MDOF systems using multiple
time scales. Part II: Nonautonomous systems,''
Commun. Nonl. Sci. Numer. Simulat., 11(1), 4581, 2006. 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,
``A simple and efficient method for computing center manifold and normal
forms associated with semisimple cases,''
Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) B: Appl. Algorithms., 10(2), 273286, 2003. PDF file
 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), 181193, 2003. PDF file
 P. Yu,
``Analysis on double Hopf bifurcation using computer algebra with the aid
of multiple scales,''
Nonlinear Dyn., 27, 1953, 2002. PDF file
 P. Yu, W. Zhang and Q. Bi,
``Vibration analysis on a thin plate with the aid of computation of normal
forms,''
Int. J. NonLinear Mech., 36(4), 597627, 2001. PDF file
 P. Yu,
``Symbolic computation of normal forms for resonant double
Hopf bifurcations using multiple time scales,''
J. Sound & Vib., 247(4), 615632, 2001. PDF file
 Q. Bi and P. Yu,
``Symbolic software development for computing the normal forms of double
Hopf bifurcation,''
J. Math. Computer Modelling, 29(9), 4970, 1999. PDF file
 Q. Bi and P. Yu,
``Symbolic computation of normal forms for semisimple cases,''
J. Comput. Appl. Math., 102(2), 195220, 1999. PDF file
 Q. Bi and P. Yu,
``Computation of normal forms of differential equations associated with
nonsemisimple zero eigenvalues,''
Int. J. Bifurcation and Chaos, 8(12), 22792319, 1998.
PDF file
 P. Yu,
``Computation of normal forms via a perturbation technique,''
J. Sound Vib., 211(1), 1938, 1998. PDF file

Flowinduced Vibration and Cable Dynamics
 Z. Xu, H. Hangan and P. Yu,
``Analytical solutions for invisicid Gaussian impinging jets,''
ASME J. Appl. Mech., 75(2), 021019, 112, 2008. PDF file
 P. Yu and K. Pan,
``Direct perturbation analysis on cables with concentrated loads'',
Commun. Nonl. Sci. Numer. Simulat., 8(2), 97112, 2003. 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, N. Popplewell and A.H. Shah,
``The KrylovBogoliubov and Galerkin methods for Nonlinear Oscillations,''
J. Sound & Vib., 192(2), 413438, 1996.
PDF file
 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), 469489, 1996. PDF file
 P. Yu, P.S. Wong and F. Kaempffer,
``Tension of conductor under concentrated loads,''
ASME J. Appl. Mech., 62(3), 802809, 1995.
PDF file
 Y.M. Desai, P. Yu, N. Popplewell and A.H. Shah,
``Finite element modeling of overhead transmission line galloping,''
Comput. Struct., 57(3), 407420, 1995. PDF file
 P. Yu, N. Popplewell and A.H. Shah,
``Instability trends of inertially coupled galloping, Part I: initiation,''
J. Sound & Vib., 183(4), 663678, 1995. PDF file
 P. Yu, N. Popplewell and A.H. shah,
``Instability trends of inertially coupled
galloping, Part II: periodic vibrations,''
J. Sound & Vib., 183(4), 679691, 1995. 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 file
 P. Yu, Y.M. Desai, N. Popplewell and A.H. Shah,
``Three degreesoffreedom model for galloping, Part II: solutions,''
ASCE J. Engng. Mech., 119(12), 24262448, 1993. PDF file
 P. Yu, A.H. Shah and Popplewell,
``Inertially coupled galloping of iced conductors,''
ASME J. Appl. Mech., 59(1), 140145, 1992. PDF file
 P. Yu, N. Popplewell and A.H. Shah,
``A geometrical approach assessing instability trends for galloping,''
ASME J. Appl. Mech., 58, 784791, 1991. PDF file
 P. Yu and K. Huseyin,
``Sensitivity analysis of certain dynamic bifurcations,''
Math. & Computer Modelling, 16(10), 4558, 1992. PDF file
 P. Yu and K. Huseyin,
``On generic dynamics related to a 3fold zero eigenvalue,''
Dynam. Stabil. Syst., 5(2), 113126, 1990. PDF file
 P. Yu and K. Huseyin,
``Dynamic behavior of an autonomous system with three
pairs of pure imaginary eigenvalues,''
Int. J. Sys. Sci., 21(6), 9931024, 1990. PDF file
 K. Huseyin and P. Yu,
``On the dynamics and stability of a codimension3 autonomous system,''
Int. J. Engng. Sci., 27(5), 583604, 1989. PDF file
 P. Yu and K. Huseyin,
``Invariant tori arising at a general critical point of codimension three,''
Appl. Math. Modelling, 13(9), 506523, 1989. PDF file
 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
 P. Yu and K. Huseyin,
``Bifurcations associated with a threefold zero eigenvalue,''
Quarterly Appl. Math., 46(2), 193216, 1988. PDF file
 K. Huseyin and P. Yu,
``On bifurcations into nonresonant quasiperiodic motions,''
Appl. Math. Modelling, 12(2), 189201, 1988. PDF file
 P. Yu and K. Huseyin,
``Two and threedimensional tori bifurcating from interactions of dynamic modes,''
Int. J. Sys. Sci., 19(9), 17631780, 1988. PDF file
 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), 121, 1988. PDF file
 P. Yu and K. Huseyin,
``Static and dynamic bifurcations associated with a double zero eigenvalue,''
Dynam. Stabil. Syst., 1(1), 7386, 1986. PDF file

Dynamic Encryption Using Chaos
 X. Huang, P. Yu and W. Huang,
``Openloop frequency response for a chaotic system,''
Chinese Physics, 15(12), 28942901, 2006. 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
 B. Fraser, P. Yu and T. Lookman,
``Secure communications using chaos synchronization,''
Physics in Canada, 57(2), 155161, 2001. PDF file

Others
 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, 12731284, 2005. PDF file
 W. Yao, C. Essex, P. Yu and M. Davison,
``A measure of predictability,''
Physics Rev. E., 69, 066121: 113, 2004. PDF file
 W. Yao, P. Yu and C. Essex,
``Communication between synchronized random number generators,''
Int. J. Bifurcation and Chaos, 14(11), 39954008, 2004. PDF file
 W. Yao, C. Essex, P. Yu and M. Davison,
``Forecast entropy,''
Kebernetes: Int. J. Systems and Cybernetics, 33(5/6), 10091015, 2004. PDF file
 K. Pan and P. Yu,
``Dynamical analysis on incompressible prestressed nonlocal elastic
material'',
Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) A: Math. Anal., 10(1), 127137, 2003. PDF file