Publications

-- Peer-Reviewed

  • Relaxation oscillations and the entry-exit function in multi-dimensional slow-fast systems.
    SIAM J. Math. Anal., Accepted. [arXiv] (Jointly with Shigui Ruan)
  • A criterion for the existence of relaxation oscillations with applications to predator-prey systems and an epidemic model.
    Discrete Contin. Dyn. Syst. Ser. B, 25(4):1257-1277, 2020. [DOI] [arXiv] (Jointly with Gail S. K. Wolkowicz)
  • Number and stability of relaxation oscillations for predator-prey systems with small death rates.
    SIAM J. Appl. Dyn. Syst., 18(1):33-67, 2019. [DOI] [arXiv]
  • Growth on two limiting essential resources in a self-cycling fermentor.
    Math. Biosci. Eng., 16 (1): 78-100, 2019. [DOI] [arXiv] (Jointly with Tyler Meadows, Lin Wang, and Gail S. K. Wolkowicz)
  • On bifurcation delay: An alternative approach using Geometric Singular Perturbation Theory.
    J. Differential Equations, 262(3):1617-1630, 2017. [DOI] [arXiv]
  • Viscous singular shock profiles for a system of conservation laws modeling two-phase flow.
    J. Differential Equations, 261(4):2300-2333, 2016. [DOI] [arXiv]
  • Competitive exclusion of microbial species for a single nutrient with internal storage.
    SIAM J. Appl. Math., 68(6):1600-1617, 2008. [DOI] (Jointly with Sze-Bi Hsu)

-- Preprints

  • Viscous singular shock profiles for the Keyfitz-Kranzer system. [arXiv]

-- In Progress

  • (with Chiu-Ju Lin and Gail S. K. Wolkowicz) A decay-consistence delay model for two species competition.
  • (with Barbara Keyfitz, Maciej Krupa, and Charis Tsikkou) singular shocks in a chromatography model with mixed generalized Langmuir isotherm.

Presentations

  • Mathematics Colloquium, University of Maine
    Orono, Maine, January 2020
  • Mathematics Colloquium, University of Tennessee at Chattanooga
    Chattanooga, Tennessee, January 2020
  • 2019 Canadian Mathematical Society CMS Winter Meeting
    Toronto, Ontario, December 6-9, 2019
  • Mathematics Colloquium, Nova Southeastern University
    Fort Lauderdale, Florida, October 2019
  • SIAM Conference on Applications of Dynamical Systems
    Snowbird, Utah, May 2019
  • American Mathematical Society AMS Sectional Meeting
    Special Session on Differential Equations in Mathematical Biology
    Auburn, Alabama, March 2019
  • Applied Math Seminar, University of Miami
    Coral Gables, Florida, October 2018
  • The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    Taipei, Taiwan, July 2018
  • 2017 Canadian Mathematical Society CMS Winter Meeting
    Scientific Session on Dynamics of Microbial Systems
    Waterloo, Ontario, December 2017
  • Mathematics Colloquium, University of New Brunswick
    Fredericton, New Brunswick, October 2017
  • Applied Mathematics, Modeling and Computational Science AMMCS International Conference
    Scientific Session on Delay Equations: Theory and Applications
    Waterloo, Ontario, August 2017
  • 2016 Canadian Mathematical Society CMS Winter Meeting
    Scientific Session on Mathematical Population Biology
    Niagara Falls, Ontario, December 2016
  • Mathematical Biology Seminar, McMaster University
    Hamilton, Ontario, October 2016
  • SIAM Minisymposium on Conservation Laws with Singular Shocks
    Boston, Massachusetts, July 2016
  • Analysis of PDEs using Dynamical Systems Techniques, Boston University
    Boston, Massachusetts, June 2016
  • Differential Equation Seminar, North Carolina State University
    Raleigh, North Carolina, April 2016
  • American Mathematical Society AMS Sectional Meeting
    Special Session on Nonlinear Conservation Laws and Applications
    Las Vegas, Nevada, April 2015
  • International Council for Industrial and Applied Mathematics ICIAM Workshop
    Columbus, Ohio, May 2014 (Poster)
  • Prairie Analysis Seminar, Kansas State University
    Manhattan, Kansas, September 2013