My students, advisees, and visitors

Undergraduate Students    Graduate Students

Undergraduate students (in William and Mary unless otherwise specified)

2013-current


Jasper Short (Virginia State University)
(jointly with Zhifu Xie)
support: NSF (2016)
Topic:

Yi Zhang (class of 2017, Mathematics/Environmental Studies)
(jointly with Leah Shaw, Rom Lipcius)
Support: NSF (2016)
Topic:

Mayee Chen (high school)
Topic:

Maggie Swift (class of 2017, Mathematics)
(jointly with Leah Shaw)
Support: NSF (2015)
Topic:

Jingyi Zhou (class of 2016, Mathematics)
(jointly with Leah Shaw, Rom Lipcius)
Support: NSF (2014)
Topic:

Wade Hobson (class of 2016, Mathematics/Physics)
(jointly with Leah Shaw, Rom Lipcius)
Support: NSF (2014)
Topic:


2011-2013

Nicholas Ducharme-Barth (class of 2013, Mathematics)
(jointly with Leah Shaw, Rom Lipcius)
Support: NSF-CSUMS (2012), NSF (2013)

Current affiliation: PhD student in marine science, University of Florida
Topic: Harvesting Dynamics in Oyster Reef Sedimentation Model

Presentation: presentation in Washington area undergraduate workshop (2013)

Wei Xia (class of 2013, Mathematics and Computer Science)
(jointly with Gexin Yu)
Support: NSF (2012)

Current affiliation: PhD student in industrial engineering, Lehigh University
Topic: Further studies in eigenvalues of quantum graphs

Matt Becker (class of 2012, Mathematics)
(jointly with Leah Shaw)
Support: NSF-CSUMS (2010), NSF (2011)

Current affiliation: PhD student in applied mathematics, Rice University
Honors Thesis Synchronous Oscillatory Solutions in a Two Patch Predator-Prey Model
Committee: Junping Shi, Leah Shaw, Daniel Vasiliu, Gexin Yu

Presentation: poster presentation in 2011 Joint Mathematics Meeting (Jan/2011)
poster presentation in 2012 Joint Mathematics Meeting (Jan/2012)
presentation in Washington area undergraduate workshop (2012)

Tim Becker (class of 2012, Mathematics)
(jointly with Leah Shaw, Rom Lipcius)
Support: NSF-CSUMS (2010), Charles Center Honors Fellowship (2011)

Current affiliation: PhD student in applied mathematics, University of Maryland, College Park
Honors Thesis: A Model for Blue Crab Population in the Chesapeake Bay
Committee: Leah Shaw, Rom Lipcius, Junping Shi, Ryan Vinroot

Presentation: poster presentation in 2011 Joint Mathematics Meeting (Jan/2011)
poster presentation in 2012 Joint Mathematics Meeting (Jan/2012)
presentation in Washington area undergraduate workshop (2012)

Patrick King (class of 2013, Mathematics and Physics)
Support: NSF-CSUMS (2011)

Current affiliation: PhD student in Astronomy, University of Virginia

Honors Thesis: The Laplacian on Isotropic Quantum Graphs: Solutions and Applications
Committee: Junping Shi, Joshua Erlich, Daniel Vasiliu, Gexin Yu

Presentation: poster presentation in 2012 Joint Mathematics Meeting (Jan/2012)
presentation in Washington area undergraduate workshop (2012)


Tim McDade (class of 2012, Mathematics and Chinese)
(jointly with Leah Shaw, Rom Lipcius)
Support: NSF-CSUMS (2011)

Current affiliation: Microsoft
Honors Thesis: Analysis and Simulation of an Optimal Control Model of an Oyster Population Displaying an Allee Effect
Committee: Junping Shi, Robert Lewis, Rom Lipcius, Leah Shaw 

Before 2011
Ruoyan Sun (class of 2013, Economics and History)
(jointly with Leah Shaw)
Support: Charles Center BioMath Fellowship (2010), HHMI (2010), NSF-CSUMS (2010), NSF-UBM (2010)

Current affiliation: MS student in public health policies, John Hopkins University
Topic: Global stability in epidemic models

Presentation: poster in 4th International Conference on  Recent Advances in Applied Dynamical Systems, Jinhua, China, (June 2010)
presentation in GMU-WM 2011 spring Workshop (4/16/2011)
Publication:
1. Sun, Ruoyan, Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence. Comput. Math. Appl. 60 (2010), no. 8, 2286–2291.
2. Sun, Ruoyan; Shi, Junping Shi, Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates. Appl. Math. Comput. 218, (2011), no. 2, 280–286.

Yuanyuan Liu (class of 2010, Mathematics and Economics)
Support: Charles Center BioMath Fellowship (2009)

Current affiliation: PhD student, Economics, Georgetown University
Honor Thesis: "The Dynamical Behavior of a Two Patch Predator-Prey Model"
Committee: Junping Shi(adviser), Olivier Coibion, Lawrence Leemis, Jianjun Paul Tian

Presentation: presentation in GMU-WM 2010 spring Workshop (4/17/2010),
Publication:

Will Jordan-Cooley (class of 2010, Mathematics)
(jointly with Rom Lipcius, Leah Shaw, Jian Shen)
Support: NSF-CSUMS (2009), NSF-UBM (2009)

Current affiliation: MS student in education, Columbia University
Honor Thesis: "Bistability in Differential Equation Model of Oyster Population and Sediment Volume"
Committee: Junping Shi(adviser), Rex Kincaid, Romulad Lipcius, Leah Shaw, Jian Shen

Presentation: poster presentation in 2010 Joint Mathematics Meeting (Jan/2010), 2010 Harvey Mudd College Mathematics Conference on the Mathematics of Environmental Sustainability and Green Technology", presentation in GMU-WM 2010 spring Workshop (4/17/2010),
Publication: Jordan-Cooley, William C.; Lipcius, Romuald N.; Shaw, Leah B. Shaw; Shen, Jian; Shi, Junping, Bistability in a differential equation model of oyster reef height and sediment accumulation. J. Theor. Biol. 289, (2011), no.1, 111.

Michael Essman (class of 2010, Mathematics and Economics)
Support: NSF-CSUMS (2009), NSF-UBM (2009)

Current affiliation: Energy Analyst, North American Power


Honor Thesis: "Mathematical and Numerical Analysis of Coupled Nonlinear Schrodinger Equations"
Committee: Junping Shi(adviser), Chi-Kwon Li, Michael Lewis, Justin May

Presentation: GMU-WM 2009 Spring Workshop (3/21/2009)
poster presentation in 2010 Joint Mathematics Meeting (Jan/2010)
poster presentation in 4th International Conference on Recent Advances in Applied Dynamical Systems, Jinhua, China (June 2010)
Publication: Essman, Michael; Shi, Junping, Bifurcation diagrams of coupled Schrödinger equations. Appl. Math. Comput. 219 (2012), no. 8, 3646--3654.

Daniel Hariprasad (class of 2009, Mathematics)
Support: NSF-UBM (2008), NSF-CSUMS (2009)

Current affiliation: PhD student in applied mathematics, University of Arizona
Webpage: http://appliedmath.arizona.edu/current-students/daniel-hariprasad

Honor Thesis: "Three Pool Model of Calcium Signaling"
Committee: Junping Shi(adviser), Jianjun Paul Tian, Michael Lewis, Greg Smith

Presentation:  GMU-WM 2009 Spring Workshop (3/21/2009)
Publication: Three pool model of Calcium signaling (Daniel Hariprasad, Meagan McNulty, Junping Shi, Paul Tian) (submitted)

Jiayin Jin (class of 2009, Harbin Institute of Technology, Mathematics)

Current affiliation: PhD student in mathematics, Michigan State University
Presentation:  2008 Harbin Differential Equation Conference (Dec/2008)
Publication: Bifurcations of Patterned Solutions in Diffusive Lengyel-Epstein System of CIMA Chemical Reaction (Jiayin Jin, Junping Shi, Junjie Wei, Fengqi Yi) (submitted)

Kristina Little (class of 2006, Mathematics)

Current affiliation: Manager in BioStatistics, Illumina

Publication:  Shi, Junping; Xie, Zhifu; Little, Kristina, Cross-diffusion induced instability and stability in reaction-diffusion systems, J. Appl. Anal. Comput. 1 (2011), no. 1, 95–119.






Graduate students

PhD students (joint publication are from thesis work only)

Qingyan Shi (2016-) Tongji University
(jointly with Yongli Song)

Visiting PhD student, College of William and Mary
(September 2016-September 2018)


Wenjie Ni (2016-) Harbin Institute of Technology
(jointly with Mingxin Wang)

Visiting PhD student, College of William and Mary
(August 2016-Februry 2018)


Yan Wang (2014-)
Topic:

Sainan Wu (2014-) Harbin Institute of Technology
(jointly with Boying Wu)

Visiting PhD student, College of William and Mary
(September 2014 -September 2016)
Topic:

Publication:
  1. Wu, Sainan, Shi, Junping, Wu, Boying, Global existence of solutions to a diffusive predator-prey model with prey-taxis. J. Differential Equations. 260 (2016), no. 7, 5847--5874.
  2. Wu, Sainan; Shi, Junping; Wu, Boying, Global existence of solutions to a quasilinear attraction-repulsion chemotaxis model with growth. To appear in Comm. Pure Appl. Anal.

Fangfang Jiang (2015) Tongji University
(adviser: Jitao Sun)

Visiting PhD student, College of William and Mary
(January 2015-April 2015)
Current affiliation: Jiangnan University
Topic:

  1. Jiang, Fangfang; Shi, Junping; Sun, Jitao, On the number of limit cycles for discontinuous generalized Lienard polynomial differential systemsInternat. J. Bifur. Chaos Appl. Sci. Engrg. 25 (2015), no. 10, 1550131 (10 pages).
  2. Jiang, Fangfang; Shi, Junping; Wang, Qing-Guo; Sun, Jitao, On the existence and uniqueness of limit cycle for a Lienard system with a discontinuity line. Comm. Pure Appl. Anal. 15 (2016), no. 6, 2509 - 2526.


Renhao Cui (2010-2014) Harbin Institute of Technology
(jointly with Boying Wu)

Current affiliation: Associate Professor, Harbin Normal University
Thesis: 

Publication:
  1. Cui, Renhao; Shi, Junping; Wu, Boying, Strong Allee effect in a diffusive predator-prey system with a protection zone. J. Differential Equations. 256 (2014), no. 1, 108--129.

Shanshan Chen (2009-2012) Harbin Institute of Technology (jointly with Junjie Wei)

Visiting Phd Student, College of William and Mary
(August 2010-August 2011)

Current affiliation: Associate Professor, Harbin Institute of Technology
Thesis: Dynamical analysis on some delayed reaction-diffusion equations

Publication:
  1. Chen, Shanshan; Shi, Junping, Global stability in a diffusive Holling-Tanner predator-prey model. Appl. Math. Lett., 25,  (2012), no. 3, 614--618.
  2. Chen, Shanshan; Shi, Junping; Wei, Junjie, A Note on Hopf bifurcations in a delayed diffusive Lotka-Volterra predator-prey system. Comput. Math. Appl. 62, (2011), no.5, 2240–2245.
  3. Chen, Shanshan; Shi, Junping; Wei, Junjie, Global stability and Hopf bifurcation in a delayed diffusive Leslie-Gower predator-prey system. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 3, 1250061, 11 pp.
  4. Chen, Shanshan; Shi, Junping; Wei, Junjie, The effect of delay on a diffusive predator-prey system with Holling type-II predator functional response. Comm. Pure Appl. Anal. 12 (2013), no. 1, 481--501.
  5. Chen, Shanshan; Shi, Junping, Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect. J. Differential Equations 253 (2012), no. 12, 3440--3470.
  6. Chen, Shanshan; Shi, Junping, Global Attractivity of Equilibrium in Gierer-Meinhardt System with Activator Production Saturation and Gene Expression Time Delays. Nonlinear Anal. Real World Appl. 14 (2013), no. 4, 1871--1886.
  7. Chen, Shanshan; Shi, Junping; Wei, Junjie, Time delay induced instabilities and Hopf bifurcations in general reaction-di ffusion systems. Journal of Nonlinear Science. 23 (2013), no. 1, 1--38.

Yuhua Zhao (2007-2012) Northeast Normal University
(jointly with Yuwen Wang)

Current affiliation: Lecturer, Harbin Normal University
Thesis: The Structure of the Extremal Solutions Set of Ill-Posed Equations in Banach Spaces and Its Applications in a System of an Autocatalytic Chemical Reaction Model

Publication:
  1. Zhao, Yuhua; Wang, Yuwen; Shi, Junping, Steady states and dynamics of an autocatalytic chemical reaction model with decay. J. Differential Equations 253 (2012), no. 2, 533–552.

Jinfeng Wang (2007-2011) Harbin Institute of Technology
(jointly with Junjie Wei)

Current affiliation: Associate Professor, Harbin Normal University
Thesis:  Dynamics of Predator-Prey System with Strong Allee Effect

Publication:
  1. Wang, Jinfeng; Shi, Junping; Wei, Junjie, Predator-prey system with strong Allee effect in prey. J. Math. Biol. 62 (2011), no. 3, 291–331.
  2. Wang, Jinfeng; Shi, Junping; Wei, Junjie, Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey. J. Differential Equations 251, (2011), no. 4-5, 1276–1304.
  3. Wang, Jinfeng; Shi, Junping; Wei, Junjie, Nonexistence of periodic orbits for predator-prey system with strong Allee effect in prey populations, Electron. J. Diff. Equ., 2013 (2013), no. 164, 1--14.


Fengqi Yi (2005-2008) Harbin Institute of Technology
(jointly with Junjie Wei)

Current affiliation: Professor, Harbin Engineering University
Thesis: Bifurcation Theory and Its Applications in Semilinear Partial Differential Equations
(it was nominated for 2010 National Best PhD Thesis Award)

Publication:
  1. Yi, Fengqi; Wei, Junjie; Shi, Junping, Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system. J. Differential Equations 246 (2009), no. 5, 1944–1977. 
  2. Yi, Fengqi; Wei, Junjie; Shi, Junping, Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system. Appl. Math. Lett. 22 (2009), no. 1, 52–55.
  3. Yi, Fengqi; Wei, Junjie; Shi, Junping, Diffusion-driven instability and bifurcation in the Lengyel-Epstein system. Nonlinear Anal. Real World Appl. 9 (2008), no. 3, 1038–1051.


Ping Liu (2005-2008) Northeast Normal University
(jointly with Yuwen Wang)

Current affiliation: Professor, Harbin Normal University
Thesis: Quasi-Linear Generalized Inverse and Imperfect Bifurcation Theory and Their Applications

Publication:
  1. Liu, Ping; Shi, JunPing; Wang, YuWen, Exact multiplicity of solutions to perturbed logistic type equations on a symmetric domain. Sci. China Ser. A 51 (2008), no. 10, 1753–1762.
  2. Liu, Ping; Shi, Junping; Wang, Yuwen, Imperfect transcritical and pitchfork bifurcations. J. Funct. Anal. 251 (2007), no. 2, 573–600.
Other PhD students I have worked with:
Ying Su, Harbin Institute of Technology
  1. Su, Ying; Wei, Junjie; Shi, Junping, Hopf bifurcations in a reaction-diffusion population model with delay effect. J. Differential Equations 247 (2009), no. 4, 1156–1184. 
  2. Su, Ying; Wei, Junjie; Shi, Junping, Bifurcation analysis in a delayed diffusive Nicholson's blowflies equation. Nonlinear Anal. Real World Appl. 11 (2010), no. 3, 1692–1703.
  3. Su, Ying; Wei, Junjie; Shi, Junping, Hopf bifurcation in a diffusive Logistic equation with mixed delayed and instantaneous density dependence. J. Dyn. Diff. Equat. 24 (2012), no. 4, 897--925.
Xin Li, Harbin Institute of Technology
  1. Li, Xin; Jiang, Weihua; Shi, Junping, Hopf bifurcation and Turing instability in the reaction–diffusion Holling–Tanner predator–prey model. IMA Journal of Applied Mathematics. 78 (2013), no. 2,  287--306.
Yong-Li Tang, National Central University
  1. Chern, Jann-Long; Tang, Yong-Li; Lin, Chang-Shou; Shi, Junping, Existence, uniqueness and stability of positive solutions to sublinear elliptic systems. Proc. Roy. Soc. Edinburgh Sect. A 141 (2011), no. 1, 45–64, 
  2. Chen, Zhi-You; Chern, Jann-Long; Shi, Junping; Tang, Yong-Li, On the uniqueness and structure of solutions to a coupled elliptic system. J. Differential Equations 249 (2010), no. 12, 3419–3442.


Master Students: (to be added)



Some pictures with students and advisees (use "view image" for larger pictures)