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