PhD students

Qingyan Shi (2016-2019) Tongji University
(jointly with Yongli Song)

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

Current affiliation: Jiangnan University
 Thesis: Spatiotemporal Pattern formation in reaction-diffusion equations with time delay and nonlocal effect

Publication:
  1. Shi, Qingyan; Shi, Junping; Song, Yongli, Hopf bifurcation in a reaction-diffusion equation with distributed delay and Dirichlet boundary condition. J. Differential Equations. 263 (2017), no. 10, 6537--6575.
  2. Shi, Qingyan; Shi, Junping; Song, Yongli, Hopf bifurcation and pattern formation in a diffusive delayed logistic model with spatial heterogeneity. Disc. Cont. Dyna. Syst. B. 24 (2019), no. 2, 467--486.

Wenjie Ni (2016-2018) Harbin Institute of Technology
(jointly with Mingxin Wang)

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

Current Affiliation: University of New England, Australia
 Thesis: Qualitative analysis of two classes of reaction-diffusion models

Publication:
  1. Ni, Wenjie; Shi, Junping; Wang, Mingxin, Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model. J. Differential Equations. 264 (2018), no. 11, 6891--6932.

Yan Wang (2014-2019) College of William and Mary

Current affiliation: Beijing Normal University
 Thesis: Persistence and extinction dynamics in reaction-diffusion-advection stream population model with Allee effect growth

Publication:
  1. Wang, Yan; Shi, Junping; Wang, Jinfeng, Persistence and extinction of population in reaction–diffusion–advection model with strong Allee effect growth. J. Math. Biol. 78 (2019), no. 7, 2093--2140.
  2. Wang, Yan; Shi, Junping, Persistence and extinction of population in reaction-diffusion-advection model with weak Allee effect growth. SIAM J. Appl. Math. 79 (2019), 1293--1313.
  3. Wang, Yan; Shi, Junping, Dynamics of a Reaction-Diffusion Benthic-Drift Model with Strong Allee Effect Growth. J. Differential Equations. 269 (2020), 7605--7642.

Sainan Wu (2014-2017) Harbin Institute of Technology (jointly with Boying Wu)

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

Current affiliation: Nanjing University Posts and Telecommunications
 Thesis: Dynamic studies on some mathematical models with taxis

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. Comm. Pure Appl. Anal. 16 (2017), no. 3, 1037-1058.
  3. Wu, Sainan; Shi, Junping; Wang, Jinfeng, Dynamics and Pattern Formation of a Diffusive Predator-Prey Model with Predator-Taxis. Math. Models Meth. Appl. Sci. 28 (2018), no. 1, 2275--2312.

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: Limit cycles in planar systems with discontinuity
  1. Jiang, Fangfang; Shi, Junping; Sun, Jitao, On the number of limit cycles for discontinuous generalized Lienard polynomial differential systems.  Internat. 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:  Semilinear elliptic equation in ecological models

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: Associate Professor, 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: 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, Dalian Technology 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.

Chenwei Tian, UC Riverside

  1. Tian, Chenwei; Shi, Qingyan; Cui, Xinping; Guo, Jingzhe; Yang, Zhenbiao; Shi, Junping, Spatiotemporal dynamics of a reaction-diffusion model of pollen tube tip growth. J. Math. Biol. 79 (2019), 1319--1355.

Sofya Zaytseva, William & Mary

  1. Zaytseva, Sofya;  Shi, Junping; Shaw, Leah, Model of pattern formation in marsh ecosystems with nonlocal interactions.  J. Math. Biol. 80 (2020), 655--686.