Publications (1986 - 2021)

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• Mathematical Biology

1. C. Gao, F. Chen and P. Yu, "Dynamics analysis in a delayed glucose-insulin model incorporating obesity," Int. J. Biomath. (in press). PDF file

2. S. Zhao, P. Yu, W. Jiang and H. Wang, "A new mechanism revealed by cross-diffusion-driven instabilities and double-Hopf bifurcation in the Brusselator system," J. Nonlinear Sci., (accepted for publication) PDF file

3. H. Cao, J. Li and P. Yu, "Study of immune response in a latent tuberculosis infection model," Commun Nonlinear Sci Numer Simulat., 140(1), 108404, 2025 (17 pages). PDF file

4. B. Zeng,P. Yu and M. Han, "An efficient solution procedure for solving higher-codimension Hopf and Bogdanov–Takens bifurcations," Commun Nonlinear Sci Numer Simulat. 138, 108241, 2024 (24 pages). PDF file

5. P. Yu, P. Pooladvand, M.M. Tanaka and L. Wahl, "Extinctions caused by host-range expansion," SIAM J. Appl. Dyn. Sys., 23(2), 1017-1703, 2024. Paper PDF file Supplement PDF file

6. Y. Zeng and P. Yu, "Multistable states in a predator–prey model with generalized Holling type III functional response and a strong Allee effect," Commun Nonlinear Sci Numer Simulat., 131, 107846, 2024 (18 pages). PDF file

7. W. Lou, P. Yu, J.F. Zhang and C. Arancibia-Ibarra, "Local and global dynamics of a ratio-dependent Holling-Tanner predator-prey model with strong Allee effect," Int. J. Bifurcation and Chaos 34(7), 2450092, 2024 (25 pages). PDF file

8. C. Gao, F. Chen and P. Yu, "Dynamics of a new delayed glucose-insulin model with obesity," Int. J. Bifurcation and Chaos 34(6), 2450070, 2024 (24 pages). PDF file

9. S.R. Zhao, P. Yu and H.B. Wang, "Spatiotemporal patterns in a Lengyel-Epstein model near a Turing-Hopf singular point," SIAM J. Appl. Math., 84(2), 338-361, 2024. Paper (size too large to upload) Supplement PDF file

10. Y. Zeng and P. Yu, "Complex dynamics of predator-prey systems with the Allee effect," Int. J. Bifurcation and Chaos 32(13), 2250203, 2022 (35 pages). PDF file

11. B. Zeng, P. Yu, "A hierarchical parametric analysis on Hopf bifurcation of an epidemic model," Discrete Contin. Dyn. Syst. Ser. S 16(3&4), 708-724, 2023. (Early access: March 2022). PDF file

12. P. Yu, M. Han and W. Zhang, "Multiple recurrent outbreak cycles in an autonomous epidemiological model due to multiple limit cycle bifurcation," J. Appl. Anal. Comp. 10(5), 2278-2298, 2020. PDF file

13. W. Zhang and P. Yu, "Revealing the role of the effector-regulatory T cell loop on autoimmune disease symptoms via nonlinear dynamics," Commun Nonlinear Sci Numer Simulat. 93, 105529, 2021. PDF file

14. M. Lu, J. Huang, S. Ruan and P. Yu, "Global dynamics of a susceptible-infectious-recovered epidemic model with a generalized nonmonotone incidence rate," J. Dyn. Differ. Equ., 33, 1625-1661, 2021. PDF file

15. Y. Xu, Y. Yang, F. Meng and P. Yu, "Modelling and analysis of recurrent autoimmune disease," Nonlinear Analysis: Real World Appl., 54, 103109, 2020. PDF file

16. J. Jiang, W. Zhang and P. Yu, "Tristable phenomenon in a predator-prey system arsing from multiple limit cycles bifurcation," Int. J. Bifurcation and Chaos 30(9), 2050129, 2020 (23 pages). PDF file

17. P. Yu and W. Zhang, "Complex dynamics in a unified SIR and HIV disease model: A bifurcation theory approach," J. Nonlinear Sci., 29(5), 2447-2500, 2019. PDF file

18. A. Zhou, X. Liu and P. Yu, "Bifurcation analysis on the effect of store-operated and receptor-operated calcium channels for calcium oscillations in astrocyte," Nonlinear Dyn. 97(1), 733-748, 2019. PDF file

19. P. Yu and X. Wang, "Analysis on recurrence behavior in oscillating networks of biologically relevant organic reactions," Math. Biosci. Eng. 16(5), 5263-5286, 2019. PDF file

20. J. Huang, S. Ruan, P. Yu and Y. Zhang, "Bifurcation Analysis of a Mosquito Population Model with a Saturated Release Rate of Sterile Mosquitoes," SIAM J. Appl. Dyn. Sys., 18(2), 939-972, 2019. PDF file Published in SIAM News Nugget "Modeling Sterile Mosquito Release to Control Disease".

21. M. Lu, J. Huang, S. Ruan and P. Yu, "Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidende rate," J. Differ. Equ., 267(3), 1859-1898, 2019. PDF file

22. B. Zeng, S. Deng and P. Yu, "Bogdanov-Takens bifurcation in predator-prey systems," Discrete Contin. Dyn. Syst. Ser. S, 13(11), 3253-3269, 2020. PDF file

23. X. Wang and P. Yu, "Complex dynamics uue to multiple limit cycle bifurcation in a tritrophic food chain model," Int. J. Bifurcation and Chaos 29(14), 1950193 (12 pages), 2019. PDF file

24. X. Zhang, Z. Jin and P. Yu, "Bifurcation of multiple limit cycles in an epidemic model on adaptive networks ,"Int. J. Bifurcation and Chaos 29(7), 1950096 (10 pages), 2019. PDF file

25. 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

26. 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

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

28. X. Sun, P. Yu and B. Qin, "Global existence and uniqueness of periodic waves in a population model with density-dependent migrations and Allee effect," Int. J. Bifurcation and Chaos, 27(12), 1750192, 2017 (10 pages). PDF file

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. X. Chen, L. Huang and P. Yu, "Dynamic behaviour of a class of HIV compartmental models," Commun. Nonl. Sci. Numer. Simulat., 23(1-3), 115-128, 2015. PDF file

36. 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

37. 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

38. 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

39. 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

40. 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 Published in SIAM News Nugget and EurekAlert and Sicence Daily "Surges in Latent Infections: Mathematical Analysis of Viral Blips".

41. 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

42. B. Chan and P. Yu, "Bifurcation analysis in a model of cytotoxic T-lymphocyte response to viralinfection," Nonlinear Analysis: Real World Appl., 13, 64-77, 2012. PDF file

43. 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

44. 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

45. 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 Syst. (DCDIS) B: Appl. Algorithms., 10(2), 317-330, 2003. PDF file

46. 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

47. 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

• Travelling Wave

1. Q. Wang, Y. Xiong, W. Huang, P. Yu, "Isolated periodic wave solutions arising from Hopf and Poincare bifurcations in a class of single species model," J. Differ. Equ. 311, 59-80, 2022. PDF file

2. X. Sun, Y. Zeng and P. Yu, "Analysis and simulation of periodic and solitary waves in nonlinear dispersive-dissipative solids," Commun Nonlinear Sci Numer Simulat., 102, 105921, 2021. PDF file

3. X. Sun and P. Yu, "Zero bifurcation diagrams for Abelian integrals: A study on higher-order hyperelliptic Hamiltonian systems with three perturbation parameter," J. Appl. Anal. Comp. 10(6), 2734-2755, 2020. PDF file

4. Y. Zeng, X. Sun and P. Yu, "Dynamical analysis on traveling wave of a reaction-diffusion model," Appl. Math. Lett., 109, 106550, 2020. PDF file

5. X. Sun and P. Yu, "Periodic traveling waves in a generalized BBM equation with weak backward diffusion and dissipation terms," Discrete Contin. Dyn. Syst. Ser. B, 24(2), 965-987, 2019. PDF file

6. X. Sun, P. Yu and B. Qin, "Global existence and uniqueness of periodic waves in a population model with density-dependent migrations and Allee effect," Int. J. Bifurcation and Chaos, 27(12), 1750192, 2017 (10 pages).

• Hilbert's 16th Problem and Limit Cycles Theory

1. T. Chen, F. Li, P. Yu, "Nilpotent center conditions in cubic switching polynomial Lienard systems by higher-order analysis," J. Differ. Equ. 379(1), 258-289, 2024 (Online Oct. 18, 2023). PDF file

2. F. Li, T. Chen, Y. Liu and P. Yu, "A complete classification on the center-focus problem of a generalized cubic Kukles system with a nilpotent singular point," Qual. Theory Dyn. Syst., 23(1), 8, 2024 (35 pages) (Online Sept. 22, 2023). PDF file

3. F. Li, Y. Wu and P. Yu, "Complete classification on center of cubic planar systems symmetric with respect to a straight line," Commun Nonlinear Sci Numer Simulat., 120, 107167 (13 pages), 2023. PDF file

4. T. Chen, L. Huang, P. Yu, "Center condition and bifurcation of limit cycles for quadratic switching systems with a nilpotent equilibrium point," J. Differ. Equ. 303(5), 326-368, 2021. PDF file

5. F. Li, Y.Y. Li, P. Yu and J. Wang, "Complex integrability and linearizability of cubic Z2-equivariant systems with two 1:q resonant singular points," J. Differ. Equ. 300(5), 786-813, 2021. PDF file

6. J. Yang, P. Yu and M. Han, "On the Melnikov functions and limit cycles near a double homoclinic loop with a nilpotent saddle of order m," J. Differ. Equ. 291(5), 27-56, 2021. PDF file

7. P. Yu, M. Han and X. Zhang, "Eighteen limit cycles around two symmetric foci in a cubic planar switching polynomial system," J. Differ. Equ., 275(2), 939-959, 2021. PDF file

8. X. Sun, Z. Chen and P. Yu, "Parameter identification on Abelian integrals to achieve Chebyshev property to achieve Chebyshev property,"Discrete Contin. Dyn. Syst. Ser. B 26(10), 5661-5679, 2021. PDF file

9. X. Sun and P. Yu, "Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop," J. Differ. Equ. 269(11), 9224-9253, 2020. PDF file

10. F. Li, Y. Jin, Y. Tian and P. Yu, "Integrability and linearization conditions of cubic Z2 systems with non-resonant singular points," J. Differ. Equ. 269(10), 9026-9049, 2020. PDF file

11. P. Yu and Y. Zeng, "Visualization of four Limit cycles in quadratic systems," Int. J. Bifurcation and Chaos 30(15), 2050236 2020 (11 pages). PDF file

12. H. Li, F. Li and P. Yu, "Dynamics and bifurcation study on an extended Lorenz system," J. Nonlinear Modeling and Analysis, 2(1), 57-78, 2020. PDF file

13. F. Li, Y.R. Liu, Y.Y. Liu and P. Yu, "Complex isochronous centers and linearization transformations for cubic Z2-equivariant planar systems," J. Differ. Equ. 268(7), 3819-3847, 2020. PDF file

14. L. Guo, P. Yu and Y. Chen, "Identifying weak focus and center in a convection model," Appl. Math. Lett., 100, 106019, 2020. PDF file

15. X. Sun and P. Yu, "Exact bound on the number of zeros of Abelian integrals for two hyper-elliptic Hamiltonian systems of degree 4," J. Differ. Equ. 267(12), 7369-7384, 2019. PDF file

16. L. Guo, P. Yu and Y. Chen, "Bifurcation analysis on a class of three-dimensional quadratic systems with twelve limit cycles," Appl. Math. Comput., 363, 124577, 2019. PDF file

17. L. Guo, P. Yu and Y. Chen, "Bifurcation analysis on a class of Z2-equivariant cubic switching systems showing eighteen limit cycles," J. Differ. Equ., 266(2-3), 1221-1244, 2019. PDF file

18. J. Yang, P. Yu and M. Han, "Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order m," J. Differ. Equ., 266(1), 455-492, 2019. PDF file

19. F. Li, Y.R. Liu, Y.Y. Liu and P. Yu, "Bi-center problem and bifurcation of limit cycles from nilpotent singular points in Z2-equivariant cubic vector fields," J. Differ. Equ. 265(10), 4965-4992, 2018.--> PDF file

20. L. Guo, P. Yu and Y. Chen, "Twelve limit cycles in 3-d quadratic vector fields with Z3 symmetry," Int. J. Bifurcation and Chaos 28(11), 1850139 (14 pages), 2018. PDF file

21. P. Yu, M. Han and J. Li, "An improvement on the number of limit cycles bifurcating from a non-degenerate center of homogeneous polynomial systems," Int. J. Bifurcation and Chaos 28(6), 1850078, 2018 (31 pages). PDF file

22. J. Yang, P. Yu and X. Sun, "On the independent perturbation parameters and the number of limit cycles of a type of polynomial Linard system," J. Math. Anal. Appl.464(1), 679-692, 2018. PDF file

23. Y. Tian and P. Yu, "Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis," J. Differ. Equ. 264(9), 5950-5976, 2018. PDF file

24. T. Chen, L. Huang, P. Yu and W. Huang, "Bifurcation of limit cycles at infinity in piecewise polynomial systems," Nonlinear Analysis: Real World Appl., 41, 82-106, 2018. PDF file

25. 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

26. X. Sun, N. Wang and P. Yu, "The monotonicity of ratios of some Abelian integrals," Bull. Sci. Math. 166, 102934, 2021. PDF file

27. 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

28. Y. Tian and P. Yu, "Bifurcation of ten small-amplitude limit cycles by perturbing a quadratic Hamiltonian system with cubic polynomials," J. Differ. Equ., 260(2), 971-990, 2016. PDF file

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. P. Yu and M. Han, "Bifurcation of limit cycles in 3rd-order Z2 Hamiltonian planar vector fields with 3rd-order perturbations," Commun. Nonl. Sci. Numer. Simulat., 18(4), 978-988, 2013. PDF file

36. 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

37. 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

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

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

40. P. Yu, M. Han and J. Li, "Bifurcation of limit cycles in cubic integrable Z2-equivariant planar vector fields," Qual. Theory Dyn. Syst., 9(1-2), 221-233, 2010. PDF file

41. 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

42. 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

43. 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

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 file

45. 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 P>
46. 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 Syst. B: Appl. & Algorithms, 15(1), 57-74, 2008. PDF file

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

48. 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), 2169-2174, 2007.

49. 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.

50. P. Yu and M. Han, "On limit cycles of the Lienard equations with Z2 symmetry," Chaos, Solitons and Fractals, 33(1), 617-630, 2007.

51. W. Yao and P. Yu, "Bifurcation of small limit cycles in Z5-equivariant planar vector fields of order 5," J. Math. Anal. Appl., 328(1), 400-413, 2007.

52. S. Wang, P. Yu and J. Li, "Bifurcation of limit cycles in a Z10-equivariant vector fields of degree 9," Int. J. Bifurcation and Chaos, 16(8), 2309-2324, 2006.

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

54. 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.

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

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

57. 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.

58. 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.

59. P. Yu and M. Han, "Small limit cycles from fine focus points in cubic order Z2-equivariant vector fields," Chaos, Solitons and Fractals, 24(1), 329-348, 2005.

60. P. Yu and M. Han, "Twelve limit cycles in a 3rd-order planar system with Z2 symmetry," Commun. Pure Appl. Anal., 3(3), 515-526, 2004.

61. 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.

62. 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.

• Nonlinear Dynamics and Chaos

1. P. Yu, M. Han and Y. Bai, "Dynamics and bifurcation study on an extended Lorenz system," J. Nonlinear Modeling and Analysis, 1(1), 107-128, 2019. PDF file

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

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

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

14. 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

15. 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.

16. Y. Shi and P. Yu, "On chaos of the logistic maps," Dynamics of Continuous, Discrete and Impulsive Syst. B: Appl. & Algorithms, 14(2), 175-195, 2007.

17. 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.

18. 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.

19. 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.

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

21. 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.

22. 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.

23. 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.

24. 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.

25. 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.

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

27. 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.

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

29. 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.

30. W. Yao, C. Essex and P. Yu, "A new chaotic system for better secure communication", Dynamics of Continuous, Discrete and Impulsive Syst. (DCDIS) B: Appl. Algorithms., 10(2), 221-234, 2003.

31. 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.

32. Q. Bi and P. Yu, "Double Hopf bifurcations and chaos of a nonlinear vibration system," Nonlinear Dyn., 19(4), 313-332, 1999.

• Stability and Bifurcation

1. B. Zeng and P. Yu, "Analysis of zero-Hopf bifurcation in two Rossler systems using normal form theory,"Int. J. Bifurcation and Chaos 30(16), 2030050, 2020 (14 pages). PDF file

2. 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

3. 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

4. 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

5. 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.

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

7. 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.

8. 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.

9. Z. Chen and P. Yu, "Hopf bifurcation control for an Internet congestion model," Int. J. Bifurcation and Chaos, 15(8), 2643-2651, 2005.

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

11. 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.

12. 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.

13. 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.

14. 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.

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

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

17. 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.

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

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

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

21. 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.

22. 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.

23. 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.

24. 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.

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

26. P. Yu and K. Huseyin, "On phase-locked motions associated with strong resonance," Quarterly Appl. Math., 51(1), 91-100, 1993.

• Non-smooth Dynamical Systems

1. F. Li and P. Yu, "A note on the paper ``Center and isochronous center conditions for switching systems associated with elementary singular points``," Commun Nonlinear Sci Numer Simulat., 90, 105405, 2020. PDF file

2. 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., 61(7), 1201-1218, 2018. PDF file

3. 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

4. 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

5. Y. Tian and P. Yu, "Center conditions in a switching Bautin system," J. Differ. Equ., 259(3), 1203-1226, 2015. PDF file

• Delay Differential Systems

1. C. Zhang, B. Zheng and P. Yu, "Second-order normal forms for n-dimensional systems with a nilpotent point," J. Appl. Anal. Comp. 10(5), 2233-2262, 2020. PDF file

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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.

14. W. Yao, P. Yu and C. Essex, "Delayed stochastic differential model for quiet standing," Physical Rev. E, 63, 021902, 2001.

• The Simplest Normal Forms

1. M. Gazor and P. Yu, "Spectral sequences and parametric normal forms," J. Differ. Equ., 252, 1003-1031, 2012. PDF file

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

3. 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

4. P. Yu and R. Chen, "The simplest parametrized normal forms of Hopf and generalized Hopf bifurcations," Nonlinear Dyn., 50(1-2), 297-313, 2007.

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

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

7. 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.

8. 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.

9. 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.

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

11. 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.

12. P. Yu and Y. Yuan, "The simplest normal forms associated with a triple zero eigenvalue of indices one and two," Nonlinear Analysis, Theory Methods Appl., 47(2), 1105-1116, 2001.

13. 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.

14. 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 Syst. (DCDIS) B: Appl. Algorithms., 8, 219-249, 2001.

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

• Conventional Normal Forms

1. 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

2. 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

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

4. P. Yu and A. Leung, "Normal forms of vector fields with perturbation parameters," Chaos, Solitons and Fractals, 34(2), 564-579, 2007.

5. 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.

6. 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.

7. 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 Syst. (DCDIS) B: Appl. Algorithms., 10(2), 273-286, 2003.

8. S. Zhu and P. Yu, "An algorithm for computing normal forms using perturbation technique", Dynamics of Continuous, Discrete and Impulsive Syst. (DCDIS) B: Appl. Algorithms., 10(2), 181-193, 2003.

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

10. 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.

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

12. 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.

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

14. 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.

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

• Flow-induced Vibration and Cable Dynamics

1. 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

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

3. P. Yu, "Explicit vibration solutions of a cable under complicated loads," ASME J. Appl. Mech., 64(4), 957-964, 1997.

4. 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.

5. 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.

6. P. Yu, P.S. Wong and F. Kaempffer, "Tension of conductor under concentrated loads," ASME J. Appl. Mech., 62(3), 802-809, 1995.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. P. Yu, A.H. Shah and Popplewell, "Inertially coupled galloping of iced conductors," ASME J. Appl. Mech., 59(1), 140-145, 1992.

13. P. Yu and K. Huseyin, "Sensitivity analysis of certain dynamic bifurcations," Math. & Computer Modelling, 16(10), 45-58, 1992.

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

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

16. 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.

17. 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.

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

19. P. Yu and K. Huseyin, "A perturbation analysis of interactive static and dynamic bifurcations," IEEE Trans. Automat. Contr., 33(1), 28-41, 1988.

20. 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.

21. P. Yu and K. Huseyin, "Bifurcations associated with a three-fold zero eigenvalue," Quarterly Appl. Math., 46(2), 193-216, 1988.

22. K. Huseyin and P. Yu, "On bifurcations into non-resonant quasi-periodic motions," Appl. Math. Modelling, 12(2), 189-201, 1988.

23. 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.

24. 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.

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

• Dynamic Encryption Using Chaos

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

2. B. Fraser, P. Yu and T. Lookman, "Steps towards improving the security of chaotic encryption," Physical Rev. E, 66, 017202, 2002.

3. B. Fraser, P. Yu and T. Lookman, "Secure communications using chaos synchronization," Physics in Canada, 57(2), 155-161, 2001.

• Others

1. 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.

2. W. Yao, C. Essex, P. Yu and M. Davison, "A measure of predictability," Physics Rev. E., 69, 066121: 1-13, 2004.

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

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

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