Sze-Bi Hsu
Department of Mathematics
National Tsing-Hua University
Hsinchu, Taiwan 300
Email:
sbhsu@math.nthu.edu.tw
Education
|
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
Award
2022 TWSIAM 第一屆會士
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
Books
|
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
II.: Chaotic Vibrating Strings
III.: Mechanics and Gas Dynamics
‘Dynamics of drug-on and drug-off models with mutation in Morbidostat ‘ to appear in Canadian Journal of Mathematics and Science 2023. PDF
On the three dimensional competition systems arising from Arabidopsis clock. (Jointly with Chao-ping Hsu).DCDS-B Vol 28, No.7 ,p.3925-3954 (2023) PDF
“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
"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
"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
"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
"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
"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
"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
“Mathematical 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
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
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
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
A survey of Mathematical Models with Variable Quota,
Taiwanese Journal of Mathematics ,Vol. 23, No.2, p. 269-291 (2019)
PDF
Mathematical Analysis on a Droop Model with
Intraguild Predation, Taiwanese Journal of Mathematics ,Vol. 23,
No.2, p. 351-373 (2019) PDF
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
A reaction–diffusion model of harmful algae and zooplankton , (with Feng-Bin Wang and Xiao-Qiang Zhao), JMAA, 451(2017) 659-677) PDF
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
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
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
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
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
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
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
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
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
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
"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
"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
"MULTIPLE
STEADY-STATES IN PHYTOPLANKTON POPULATION INDUCED BY
PHOTOINHIBITION" ( with YIHONG DU, YUAN LOU), JDE.258(201)
2408-2434 PDF
"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
"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
"FURTHER
STUDIES OF A REACTION-DIFFUSION SYSTEM FOR AN UNSTIRRED CHEMOSTAT
WITH INTERNAL STORAGE" (with Junping Shi and Feng-Bin Wang)
DCDS-B,19(2014),no.10 (December).PDF
"Global Dynamics of Zooplankton and Harmful Algae in
Flowing Habitats'' (with Feng-Bin Wang, Xiao-Qiang Zhao), JDE
255(2013), pp 265-297. PDF
" 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
"A Refuge-mediated Apparent Competition Model" (with Lih-Ing Wu
Roeger), Canadian Applied Math. Quaterly 19(2013) No. 3, pp
219-234. PDF
"Reaction–diffusion 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
"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
"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
"A Lotka-Volterra Competition model with season
succession" (with Xiaoqiang Zhao) J. Math. Biology (2012),
64,p.109-130 PDF
"Synchronized reproduction promotes species
coexistence through reproductive facilitation"(with Yu-Yun Chen),
J.Theoretical Biology 274(2011), pp 136-144
PDF
"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
"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
"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
"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
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
"Heteroclinic cycles in the chemostat models and the
winnerless competition principle" (with Lih-Ing W. Roeger) , JMAA,
(2009), PDF
"Relaxation oscillation profile of limit cycle in
predator-prey system" (with Junping Shi) , DCDS-B, Vol. 11 (2009),
No. 4, pp. 893-911 PDF
" 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
"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
" 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
"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
"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
"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
"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
"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
"On the Role of Asymptomatic Infection in
Transmission Dynamics of Infectious Diseases"(with Ying-Hen
Hsieh)Bulletin of Mathematical Biology (2008) 70: 134–155 PDF
"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
"The final size of a SARS epidemic model without
quarqntine" (with Lih-Ing W. Roeger), J. Math. Anal. Appl., 333,
(2007), 557-566 PDF
"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
"Constructing Lyapunov Functions for Mathematical
Models in Population Biology", Taiwanese Journal of Math., vol 9,
No.2, (2005), 151-173. PDF
"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
"A diffusive predator-prey model in heterogeneous
environment", (with Yihong Du), JDE 203(2004)
331-364. PDF
"A survey of Mathematical Models of Competition with
on inhibitor", (with Paul Waltman). Math. Biosci. 187(2004)
53-91 PDF
"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
"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
"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
"Plasmid-bearing ,plasmid-free organisms Competing
for two complementary nutrients in a chemostat" (with Yun-Huei
Tzeng) Math Bios 179 (2002)183-206 PDF
"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
"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
"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
"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
"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
"Competition in the presence of a lethal external
inhibitor",(with Yen-Sheng Li and Paul Waltman), Math. Bioscience
167(2000)177-199. PDF
"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
"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
"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
"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
"Competition between Plasmid--Bearing and
Plasmid--Free organisms in selective media", (with P. Waltman),
{\mbs Chemical Engineering Science}, Vol. 52 (1997),
23-35. PDF
"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
"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
"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
"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
"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
"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
"Dynamics of competition in the unstirred chemostat",
(with H. Smith and P. Waltman), {Canadian Appl. Math. Quarterly}
(1994), 461-483. PDF
"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
"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
"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
"A mathematical model of chemostat with periodic
washout rate", (with Butler, Waltman), {SIAM, J. Appl. math.},
Vol. 45, No. 3, (1985), 435-449. PDF
"Steady state of a system of P.D.E. modeling
microbial ecology", {SIAM J. Math. Analysis}, Vol. 14 (1983),
1130-1138. PDF
"Coexistence of competing predator in a chemostat",
(with G.J. Butler and P.E. Waltman), {J. Math. Biology}, 17
(1983), 133-151. PDF
"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
"Predator--Mediated coexistence and extinction",
{Math. Bios.}, 54 (1981), 231-248. PDF
"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
"Some results on global stability of a Predator--Prey
system", (with S.S. Lin and Cheng), {J. Math., Biology}, 12
(1981), 115-126.PDF
"On a resource based ecological competition model
with interference", {J. Math. Biology}, 12 (1981), 45-52.PDF
"A competition model for a seasonally flluctuating
nutrient", {J. Math. Biology}, 9 (1980), 115-132. PDF
"Two predators competing for two prey species_G An
analysis of MacArthur's model", (with Hubbell), {Math. Biocience}
43 (1979), 143-171. PDF
"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
"Competing predator", (with Waltman, Hubbell), {SIAM
J. Appl math.}, Vol. 135, No. 4 (1978), 617-625.PDF
"A contribution to the theory of competing
predators", (with Waltman, Hubbell), Ecological Monograph, 38
(1978), 337-349. PDF
"Limiting behavior for competing species", SIAM, J.
Appl. Math., Vol. 34, No. 4 (1978), 760-763. PDF
"On global stability of a Predator--Prey system",
Math. Bioscience, 39 (1978), 1-10. PDF
"The application of the Poincare--Transform to the
Lotka--Volterra model", J. Math. Biology, 6 (1978), 67-73. PDF
"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
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) 1457–1467 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) 1439–145 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