Sze-Bi Hsu

Department of Mathematics

National Tsing-Hua University

Hsinchu, Taiwan 300




B. S., Tsing-Hua University, Taiwan 1970

ph. D., University of Iowa, 1976

Professional Experience

Instructor, University of Utah, 1976-1979

National Chiao-Tung University

Associate Professor, 1979-1980

Professor, 1980-1985

National Tsing-Hua University

Professor, 1985--

Chairman, Institute of Applied Mathematics, 1987-1990

Dean, College of Science, 1998-2004

  Visiting Professor, University of Maryland, 1986-1987

  Visiting Professor, Emory University, 1990-1991

Visiting Professor, Texas A&M University, 2004-2005


  MOE Science Award, 2005

  MOE National Chair Professor (Feb.1,2011-Jan.31, 2014)

 Tsing-Hua Distinguished  Chair Professor (2011-)

 ROC Mathematical Society Award 2012

 SIAM Fellow 2013


Lectures on Chaotic Dynamical Systems, International Press, 2002 (with Valentine Afraimovich) 


Ordinary Differential Equations with Applications, Word Scientific Press, 2006 (First edition), 2013 (Second edition).

Lecture Notes

Mathematical Modeling and Mathematical Analysis in Mathematical Biology( Summer Course ,7/1-7/14,2019 in Harbin Institute of Technology)

Mathematical Biology for undergraduate students [DOC]

Mathematical Modelling in Biologial Science [PDF]


Journal Articles

I.: Mathematical Biology

II.: Chaotic Vibrating Strings

III.: Mechanics and Gas Dynamics

      I.         Mathematical Biology

  1. “Analysis of the Droop Model with Wall Growth in a Chemostat” (jointly with Xiaochen Duan), Taiwanese J. Math. 25 (4), 793-807, (August, 2021) .PDF

  2. "The dynamics of a two host two virus system in a chemostat environment" (jointly with Jin You), DCDS-B (2021), 26(1) p.415-441 .PDF

  3. "Competition of two host species for a single -limited resource mediated by parasites" (jointly with I-Fang Sun) Tamkang Journal of Mathematics, Tamkang J. Of Math., (2021) Vol.52, No.1, p. 1-18.PDF

  4. "A Spatiotemporal Model of Drug Resistance in Bateria with Mutations" (jointly with Jifa Jiang) Rend. Istit. Mat. UNiv. Trieste ,,vol. 52, pp.1-11 (2020).PDF

  5. "A Holling predator-prey model with handling and searching predators" ( jointly with Pierre Mahal and Zhihua Liu)
    SIAM Journal of Applied Mathematics, (2020) Vol 180, No.4, pp.1778-1795. PDF

  6. "A periodic-parabolic Droop model for two species comprtition in an unstirred chemostat" ( jointly with Xiaoqing He, Feng-Bin Wang ) DCDS-A. (2020) Vol.40, No. 7 , pp.4427-4451, PDF

  7. "Analysis of a mathematical model arising from Barnacle-Algae-Mussel interactions°® (jointly with Yi Wang and Hui Zhou) (jointly with Yi Wang and Hui Zhou) SIAM Journal of Applied Mathematics.(2019) Vol.79,No.5, pp.2032-2053. PDF

  8. °ßMathematical modeling and analysis of harmful algal blooms in flowing habitat°® ( jointly with Feng-Bin Wang and Xiaoqiang Zhao) Mathematical Bioscience and Engineering. Vol. 16, No.6, pp. 6728-6752 (2019). PDF

  9. The continuous Morbidostat : a chemostat controlled drug application to select for drug resistance mutants, (with Ya-Tang Yang and Zhenzhen Chen), CPAA AIMS (2020) 19 (1), p.203-220. PDF

  10. Global Dynamics of a reaction-diffusion system with intraguild predation and internal storage(with Nie Hua and Fenf-Bin Wang), DCDS-B (2020) 25(3), 877-901. PDF

  11. Extinction and uniform persistence with a microbial food web with mycoloop limiting behavior of a population model with parasite fungi
        (with Alex Almocera and Polly Sy), Mathematical Bioscience and Engineering 16(1), 516-737 (2018) PDF

  12. Steady state solutions of a reaction-diffusion system arising from intraguild predation and internal storage , (with Nie Hua, Feng-Bin Wang) Vol. 293, p. 1-33JDE (2019). PDF
  13. A survey of Mathematical Models with Variable Quota, Taiwanese Journal of Mathematics ,Vol. 23, No.2, p. 269-291 (2019) PDF

  14. Mathematical Analysis on a Droop Model with Intraguild Predation, Taiwanese Journal of Mathematics ,Vol. 23, No.2, p. 351-373 (2019) PDF

  15. A competition model with dynamically allocated toxin production in the unstirred chemostat, (Jointly with Hua Nie, Jianhua Wu) , Communication on pure and Applied Analysis, Vol.16, No.4, (2017), p.1373-1404. PDF

  16. A reaction°Vdiffusion model of harmful algae and zooplankton , (with Feng-Bin Wang and Xiao-Qiang Zhao), JMAA, 451(2017) 659-677) PDF

  17. Single species growth consuming inorganic carbon with internal storage in a poorly mixed habitat, (with King-Yeung Lam and Feng-Bin Wang), J.Math. Biology 75, No. 6-7, 1775-1825 (2017) PDF

  18. Numerical proof for chemostat chaos of Shilnikov type, (with Bo Deng , Maoan Han) to appear in Chaos: An Inter discuiplinary Journal of Nonlinear Science , N0.3, 033106 14pp (2017) PDF

  19. The Morbidostat: A Bio-reactor that promotes selection for dry-resistance in bacteria (with Zhenzhen Chen and Ya-Tang Yang) , SIAM J. Applied Mathematics 77-2(2017), pp.470-499. PDF

  20. Competition for two essential resources with internal storage and periodic input (with Feng-Bin Wang and Xiaoqiang Zhao) , Differential and Integral Equations(2016) vol29(7-8) p.601-630 PDF

  21. Growth of single phytoplankton species with internal storage in a water column (with Linfeng Mei, Feng-Bin Wang), DCDS-B (2016), p. 607-620 PDF

  22. Dynamics of harmful algae with seasonal temperature variation in the cove-main lake (with Wendi Wang, Feng-Bin Wang) DCDS-B Vol. 21, No.1 (2016) p. 313-335PDF

  23. On a nonlocal reaction-diffusion system modeling the growth of phytoplankton with cell quota structure (with Linfeng Mei, Feng-Bin Wang) JDE 259(2015)no. 10, p. 5353-5378PDF

  24. Algal competition in a water column with excessive dioxide in the atmosphere .(with Hua Nie and J.P.Grover) J.Math. Biology(2016) vol21,No.2 p.437-446 PDF

  25. Coexistence solutions of a competitive model with two species in a water column (with Hua Nie and Jianhua Wu), in DCDS-B 20(2015)no.8, 26941-2714PDF

  26. A reaction-diffusion-advection model of harmful algae growth with toxin degradation (with Feng-Bin Wang and Xiaoqiang Zhao), in JDE, 259(2015) p.3178-3201 PDF

  27. " Theory of a microfluidic serial dilution bioreactor for growth of planktonic and biofilm population" (with Ya-Tang Yang) J. Math. Biology 72 (2016) ,1401-1427. PDF

  28. "A pivotal eigenvalue problem in river ecology" (with J. Lopez-Gomez,Lingfen Mei,Feng-Bin Wang), JDE 29(2015)2280-2316. PDF

  29. "Analysis of three species Lotka-Volterra food web models with omnivory" (with Shigui Ruan and Ting-Hui Yang),J.Mathematical Analysis and Applications,426 (2015) 659-687. PDF

  30. "A NONLOCAL PROBLEM FROM CONSERVATION BIOLOGY" ( with J. LO_ PEZ-GO_MEZ, L. MEI, AND M. MOLINA-MEYER), SIAM Journal of Mathematical Analysis, 46-6(2014) p.4035-4059. PDF


  32. "Dynamics of two phytoplankton Species Competing for light and nutrient with internal storage." (with C.J. Lin),DCDS-S 7(2014) no.6. p.1259-1285.PDF

  33. "On the Dynamics of Two-consumers-one-resource Competing Systems with Beddington-DeAngelis Functional Response'' (with Shigui Ruan, and Ting-Hui Yang),DCDS-B, 18(2013) NO.9, pp2331-2353. PDF


  35. "Global Dynamics of Zooplankton and Harmful Algae in Flowing Habitats'' (with Feng-Bin Wang, Xiao-Qiang Zhao), JDE 255(2013), pp 265-297.  PDF

  36. " Dynamics of Phytoplankton Communities Under Photoinhibition'' (with Chiu-Ju Lin , Chih-Hao Hsieh, Kohei Yoshiyama), Bulletin of Math Biology 75(2013) No.7, p.1207-1232. PDF 

  37. "Subfunctionalization reduces the fitness cost of gene duplication in humans by buffering dosage imbalances " (with Ariel Fern_ndez, Yun-Huei Tzeng)  Genomics 2011, 12:604,  PDF 

  38. "A Refuge-mediated Apparent Competition Model" (with Lih-Ing Wu Roeger), Canadian Applied Math. Quaterly 19(2013) No. 3,  pp 219-234.  PDF

  39. "Reaction°Vdiffusion equations of two species competing for two complementary resources with internal storage"  (with Jifa Jiang and Feng-Bin Wang)  J. Diff. Equat. Vol 251(2011) pp 918-940  PDF

  40. "Competition between microorganisms for a single limiting resource with cell quota structure and spatial variation  (with James P. Grover and Feng-Bin Wang) J. Math. Biol 64(2012), No. 5, pp 713-743..  PDF

  41. "Dynamics of a Periodically Pulsed Bio-Reactor Model With a Hydraulic Storage Zone" (with Feng-Bin Wang and Xiaoqiang Zhao) J Dyn Diff Equat 23(2011), No. 4, pp 817-842.  PDF 

  42.   "A Lotka-Volterra Competition model with season succession" (with Xiaoqiang Zhao)  J. Math. Biology (2012), 64,p.109-130 PDF 

  43. "Synchronized reproduction promotes species coexistence through reproductive facilitation"(with Yu-Yun Chen), J.Theoretical Biology 274(2011), pp 136-144 PDF 

  44. "Single phytoplankton species growth with light and advection in a water column" (with Yuan Lou),  SIAM J. Appli. Math., Vol 70,(2010) No.8, pp 2942-2974  PDF

  45.   "on a system of reaction-diffusion equations arising from competition with internal storage in an unstirred chemostat" (with Jifa Jiang, Feng-Bin Wang) , JDE 248 (2010), pp 2470-2496 PDF

  46.   "On a nonlocal reaction-diffusion problem arising from the modeling phytoplankton growth" (with Yihong Du), SIAM J. Math. Analysis 42 (2010), pp 1305-1333 PDF

  47. "On a mathematical modelarising from cpmpetition of phytoplankton species for a single nutrient with internal storage: Steady state analysis." (with  Feng-Bin Wang) , Commun. Pure Appl. Anal. 10 (2011) ,no.5,1479-1501 PDF

  48.   Competition and coexistence in flowing habitats with a hydraulic storage zone" (with James P. Grover, Feng-Bin Wang) , Mathematical Biosciences, Vol. 222 (2009), pp. 42-52 PDF

  49. "Heteroclinic cycles in the chemostat models and the winnerless competition principle" (with Lih-Ing W. Roeger) , JMAA, (2009), PDF

  50. "Relaxation oscillation profile of limit cycle in predator-prey system" (with Junping Shi) , DCDS-B, Vol. 11 (2009), No. 4, pp. 893-911 PDF

  51. " Analysis of a Model of Two Parallel Food Chains" (withChristopher A. Klausmeier, Chiu-Ju Lin) , DCDS-B, Vol. 9 (2009), No. 2,pp. 337-359 PDF

  52. "Mathematical Analysi of Two Microbial Species Competing for Two Complementary Resources with Internal Storages and Different Removal, DilutionRates" (with Fern-Bin Wang) , Bulletin of the Institute of Mathematics Academia Sinica, Vol. 3 (2008), No. 4, pp. 487-508 PDF

  53.   " Non-periodicity of chemostats: a multi-dimensional negative Bendixson Dulac criterion" (with Bernold Fiedler) , J. Math. Biology, Vol. 59(2009), No. 2, pp. 233-253 PDF

  54. "Concentration Phenomena in a Nonlocal Quasilinear Problem Modelling Phytoplankton I: Existence" (with YIHONG DU) SIAM Journal of Mathematical Analysis, Vol 40, p1419-1440 (2008) PDF

  55.   "Concentration Phenomena in a Nonlocal Quasilinear Problem Modelling Phytoplankton II: Limiting Profile" (with YIHONG DU) SIAM Journal of Mathematical Analysis, Vol 40, p1441-1470 (2008) PDF

  56.   "Competitive Exclusion of Microbial Species for a Single-Nutrient with Internal Storage" (with TING-HAO HSU) SIAM. J. Appl. Math, Vol 68,(2008) No. 6, p1600-1617 PDF

  57.   "Spreading Speeds and Traveling Waves for Non-Monotone Integrodifference Equations"(with XIAO-QIANG ZHAO) SIAM J. Math. Analysis, , Vol 40,(2008) No. 2, p776-789 PDF

  58.   "Global Dynamics of a Predator-Prey Model with HASSELL-VARLEY Type Functional Response" (with Tzy-Wei Hwang, Yang Kuang) Discrete and Continuous Dynamical System, Series B, Vol 10,(2008) No. 4, p857-871 PDF

  59. "On the Role of Asymptomatic Infection in Transmission Dynamics of Infectious Diseases"(with Ying-Hen Hsieh)Bulletin of Mathematical Biology (2008) 70: 134°V155 PDF

  60. "Impact of quarantine on the 2003 SARS outbreak: A retrospective modeling study" (with Ying-Hen Hsieh et), Journal of Theoretical Biology, 244, (2007), 729-736 PDF

  61. "The final size of a SARS epidemic model without quarqntine" (with Lih-Ing W. Roeger), J. Math. Anal. Appl., 333, (2007), 557-566 PDF

  62.   "Modeling intervention measures and severity-dependent public response during severe acute respiratory Syndrome Otubreak" (with Ying-Hen Hsieh), SIAM J. Appl. Math., vol 66, No.2, (2006), 627-647   PDF

  63. "Constructing Lyapunov Functions for Mathematical Models in Population Biology", Taiwanese Journal of Math., vol 9, No.2, (2005), 151-173.   PDF

  64. "A Discrete-Delayed model with Plasmid-Bearing, Plasmid-Free Competition in a Chemostat" (with Cheng-Che Li), DCDS, vol 5, No.3, (2005), 699-718.    PDF

  65. "A diffusive predator-prey model in heterogeneous environment", (with Yihong Du), JDE 203(2004) 331-364.    PDF

  66. "A survey of Mathematical Models of Competition with on inhibitor", (with Paul Waltman). Math. Biosci. 187(2004) 53-91   PDF

  67.   "The Severe Acute Respiratory Syndrome Outbreak in Taiwan: Lesson to be learn" (with Ying-Hen Hsieh, Cathy W. S. Chen) Emerging Infectious Diseases (2004) vol 10,No.2, 201-206   PDF

  68. "Heteroclinic Foliation, Global Oscillations for the Nicholson-Bailey Model and Delay of Stability Loss" (with Ming-Chia Li, Weishi Liu, Mikhail Malkin) Discrete and c ontinuous Dynamical Systems ,vol 9,No. 6,(2003),1465-1492   PDF

  69. "A Ratio-Depentent Food Chain Model and its Application to Biological control" (with T.W.Huang ,Y.Kuang) Math.Bios.181(2003)55-83   PDF

  70. "Plasmid-bearing ,plasmid-free organisms Competing for two complementary nutrients in a chemostat" (with Yun-Huei Tzeng) Math Bios 179 (2002)183-206   PDF

  71. "A model of the effect of anti-competitor toxins on plasmid-bearing ,plasmid-free competition" (P.Waltman) Taiwanese J.Math 6(1)(2002)135-155   PDF

  72. "Rich dynamics of a ratio-dependent one prey two predator model" (with T.W.Hwang and Y.Kuang) J.Math.Biology 43 (2001), 377-396   PDF

  73. "Chaotic behavior of three competing species of May-Leonard model under small periodic perturbation ", (with V, Afraimovich, Huey-Er Lin ), International J. of Bifurcation and Chaos, Vol. 11, No. 2 (2001) 435-447.   PDF

  74. "Global Analysis of the Michaelis-Menten type ratio-dependence predator-prey system", (with T. W. Hwang and Y. Kuang), J. Math. Biol.(2001), 42, 489-506.   PDF

  75. "Stability analysis for a class of diffusive coupled system with applications to population biology ", (with Ruey-Tarng Gong), Canadian Applied Math. Quarterly (2000) Vol. 8, P. 79-96.   PDF

  76.   "Competition in the presence of a lethal external inhibitor",(with Yen-Sheng Li and Paul Waltman), Math. Bioscience 167(2000)177-199.   PDF

  77.   "Hopf Bifurcation Analysis for a Predator-Prey system of Holling and Leslie type", (with T.W. Hwang), {Taiwanese Journal of Mathematics}, (1999) Vol. 3, No. 1, p.35-53.   PDF

  78.   "Extinction of top predator in a three level food chain model", (with C.H. Chiu), {J. Math. Biology}, (1998) vol. 37, P.372-380.   PDF

  79.   "Competition in the chemostat when one competitor produces a toxin", (with P. Waltman) {Japan SIAM J. Applied Mathematics} (1998), Vol. 15, No. 3 p.471-490.   PDF

  80. "Uniqueness of limit cycles for a Predator--Prey system of Holling and Leslie type", (with T.W. Hwang), {Quarterly Canadian Applied Mathematics}, (1998) Vol. 6, No. 2, p.91-117. PDF

  81.   "Competition between Plasmid--Bearing and Plasmid--Free organisms in selective media", (with P. Waltman), {\mbs Chemical Engineering Science}, Vol. 52 (1997), 23-35.   PDF

  82.   "On the asymmetric May-Leonard model of three competing species",(with Chia-Wei Chi and Lih-Ing Wu), {SIAM J. of Applied Math.}, Vol. 58, No. 1, p.211--226 (1998).   PDF

  83.   "Competitive exclusion and coexistence for competitive system on ordered Banach space", (with H.L. Smith and P. Waltman), {AMS Transaction}, Vol. 348 (1996), 4083-4094.   PDF

  84. "Competition between Plasmid--Bearing and Plasmid--Free organisms in a chemostat with inhibitor", (with T.K. Luo and P. Waltman), {J. of Math. Biology}, Vol. 34 (1995), 225-238.   PDF

  85.   "Global analysis of a model of Plasmid--Bearing, Plasmid--Free competition in a chemostat with inhibitions", (with T.K. Luo), {J. of Math. Biology}, Vol. 34 (1995), 41-76. PDF

  86. "Global stability for a class of Predator--Prey systems", (with Tzy--Wei Huang), {SIAM J. Appl. Math.}, Vol. 55, No. 3 (1995), 763-783.  PDF

  87.   "Global analysis of a model of Plasmid--Bearing, Plasmid--Free competition in a chemostat", (with P. Waltman and G. Wolkowicz), {Journal of Mathematical Biology} 32 (1994), 731-742.  PDF

  88.   "Dynamics of competition in the unstirred chemostat", (with H. Smith and P. Waltman), {Canadian Appl. Math. Quarterly} (1994), 461-483.  PDF

  89.   "A remark on the global asymptotic stability of A dynamical system modeling two species competition", (with P.E. Waltman and S. Ellermeyer), {Hiroshima Mathematical Journal}, Vol 24. No. 2 (1994) 435-445. PDF

  90. "On a system of Reaction--Diffusion equations arising from competition in an unstirred chemostat", (with P.E. Waltman), {SIAM J. Appl. Math.}, Vol. 53, No. 4, (1993), 1026-1044. PDF

  91. "Analysis of a model of two competitors in a chemostat with an external inhibitor", (with P.E. Waltman), {SIAM J. Applied Math.}, Vol. 52, No. 2, (1992), 528-540.  PDF

  92.   "A mathematical model of chemostat with periodic washout rate", (with Butler, Waltman), {SIAM, J. Appl. math.}, Vol. 45, No. 3, (1985), 435-449.  PDF

  93.   "Steady state of a system of P.D.E. modeling microbial ecology", {SIAM J. Math. Analysis}, Vol. 14 (1983), 1130-1138.  PDF

  94. "Coexistence of competing predator in a chemostat", (with G.J. Butler and P.E. Waltman), {J. Math. Biology}, 17 (1983), 133-151. PDF

  95. "A remark on the period of periodic solutions in the Lotka--Volterra system", {J. Math. Analysis and Application}, Vol. 95, No. 2, (1983), 428-436. PDF

  96.   "Predator--Mediated coexistence and extinction", {Math. Bios.}, 54 (1981), 231-248. PDF

  97.   "Exploitative competition of two Micro--Organisms for two complementary nutrients in a continuous culture", (with Cheng, Hubbell), {SIAM J. App. Math.}, (1981), 422-444.  PDF

  98.   "Some results on global stability of a Predator--Prey system", (with S.S. Lin and Cheng), {J. Math., Biology}, 12 (1981), 115-126.PDF

  99.   "On a resource based ecological competition model with interference", {J. Math. Biology}, 12 (1981), 45-52.PDF

  100. "A competition model for a seasonally flluctuating nutrient", {J. Math. Biology}, 9 (1980), 115-132. PDF

  101. "Two predators competing for two prey species_G An analysis of MacArthur's model", (with Hubbell), {Math. Biocience} 43 (1979), 143-171.  PDF

  102. "Theoretical and experimental investigation of microbial competition in continuous culture", (with Waltman, Hubbell), {Proceeding of Conference in Biomathematics at Southern Illinois University}, edited by Burton, (1978) 107-152. PDF

  103.   "Competing predator", (with Waltman, Hubbell), {SIAM J. Appl math.}, Vol. 135, No. 4 (1978), 617-625.PDF

  104.   "A contribution to the theory of competing predators", (with Waltman, Hubbell), Ecological Monograph, 38 (1978), 337-349.  PDF

  105.   "Limiting behavior for competing species", SIAM, J. Appl. Math., Vol. 34, No. 4 (1978), 760-763.  PDF

  106.   "On global stability of a Predator--Prey system", Math. Bioscience, 39 (1978), 1-10. PDF

  107.   "The application of the Poincare--Transform to the Lotka--Volterra model", J. Math. Biology, 6 (1978), 67-73. PDF

  108.   "A mathematical theory for Single--Nutrient competition in continuous culture of Micro--Organisms", (with Waltman, Hubbell), SIAM J. Appl. Math. Vol. 32, No. 2 (1977), 366-382.  PDF

    II.         Chaotic Vibrating Strings

1.     "THE SPECTRUM OF CHAOTIC TIME SERIES (II): WAVELET ANALYSIS" (with GOONG CHEN, YU HUANG, and MARCO A. ROQUE-SOL) International Journal of Bifurcation and Chaos, Vol. 21, No. 5 (2011) 1457°V1467   PDF

2.     "THE SPECTRUM OF CHAOTIC TIME SERIES (I): FOURIER ANALYSIS" (with GOONG CHEN, YU HUANG, and MARCO A. ROQUE-SOL) International Journal of Bifurcation and Chaos, Vol. 21, No. 5 (2011) 1439°V145   PDF

3.     "Chaotic Vibration of the Wave Wquation with Nonlinear Feedback Boundary Control: Progress and Open Problems" (with Goong Chen and Jianxin Zhou) Chapter 2, Chaos Control, Vol I ,Chaos and Bifurcation Control: Theory and Applications,Edited by Guanrong Chen, Lecture Note in Control and Information Science, Springer Verlag (2003)   PDF

4.     "Analyzing Displacement Term's Memory Effect in a van der Pol Type Boundary Condition to Prove Chaotic Vibration of the Wave Equation" (with Goong Chen & Tingwen Huang)International J. of Bifurcation and Chaos vol 12 ,No5 (2002) 965-982   PDF

5.     "Nonisotropic spatiotemporal chaotic vibration on the Wave equation due to mixing energy transport and a Van der Pol boundary condition" (with Goong Chen & Jianxin Zhou)International J. of Bifurcation and Chaos vol 12,No3 (2002) 535-559   PDF

6.     "Chaotic Vibration of the Wave Equation by Nonlinear Feedback Boundary Control", Chapter 7, p.131-154, {Controlling Chaos and Bifurcation in Engineering}, CRC Press, edited by Guangrong Chen (1999). PDF

7.     "Snapback Repellers as a Cause of Chaotic Vibration of the Wave Equation with a Van Der Pol boundary condition and energy injection at the middle of the span", (with G. Chen and J. Zhou), {J. of Math. Physics} (1998) Vol. 39, No. 12, p.6459-6489.   PDF

8.     "Chaotic vibration of the one-dimensional wave equation due to a self-excitation boundary condition, Part III_G Natural hysteresis memory effects", (with G. Chen and J. Zhou), {International Journal of bifurcation and Chaos}, Vol. 8, No. 3 (1998) p.447-470.   PDF

9.     "Chaotic vibration the one-dimensional wave equation due to a self-excitation boundary condition PartII_G Energy Pumping, Period doubling and homoclinic orbits", (with G. Chen and J. Zhou), {International Journal of Bifurcation and Chaos}, Vol. 8, No. 3 (1998) p.423-445.   PDF

10.  "Chaotic vibrations of the One-Dimensional wave equation due to a Self-Excitation boundary condition, Part I_Gcontrolled hysteresis", (with G. Chen and J. Zhou), { AMS Transaction}, (1998) Vol. 350, No. 11, p.4265-4311.   PDF

11.  "Linear superposition of chaotic and orderly vibrations on two serially connected string with a van der Pol Joint", (with G. Chen and J. Zhou), {International J. of Bifurcation and chaos}, Vol. 6 (1996), 1509-1527. PDF

  III.         Mechanics and Gas Dynamics

1.     Classification of potential flows under renormalization group transforms (with Bernold Fiedler and Hsui-Hau Lin) ,Discrete Continuous Dynamical System Series B, 21(2016) no.2, 437-446.  PDF

2.     Hierarchy of relevant couplings in perturbative renormalization group transformations" (with Hong-Yan Shih, Wen-Ming Huang, and Hsiu-Hau Lin1) Physical review B 81 ([1] 2010)  PDF

3.     "Mathematical Analysis of a Bohr Atom Model" (with Goong Chen et) , to appear in Journal of Mathematical Physics ( J. Math. Physics, (2006) , Vol 47, issue 2, p. 022107). PDF

4.     "A Qualitative Study on the Damped Duffing Equation and Applications" (with Z. Feng, G. Chen), Discrete and Continuous Dynamical Systems Series B, vol. 6, No.5 (2006), 1097-1112.   PDF

5.     "On the singular behavior of v''(x)+x sin v(x)=0", (with K.S. Cheng, S.F. Hwang), Journal of Mathematical Analysis and Applications}, Vol. 163, No. 1 (1992), 20-37. PDF

6.     "Nonlinear singular Sturm--Liouville problem and application to transonic flow through a nozzle", (with Tai-Ping Liu), {\mbs Communication in Pure and Applied Mathematics}, Vol. XLIII (1990), 31-61. PDF

7.     "Uniqueness property of large deformation of a heavy cantilever",{Bulltin of the Institute of Mathematics Academia Sinica}, Vol. 17, No. 3 (1989), 193-204.  PDF

8.     "On the asymptotic behavior of solutions of v''(x) + x sin v(x)=0", (with W.M. Ni), {Bulltin of the Institute of Mathematics Academia Sinica}, Vol. 16, No. 2 (1988), 109-114. PDF

9.     "Anlaysis of large deformation of heavy cantilever", (with S.F. Hwang), {SIAM J. Math. Analysis}, Vol. 19, No. 4 (1988), 854-866.  PDF