BEWARE: I no longer work in UM since 2020.

About

I am an applied mathematician specialized in Dynamical Systems. I received my PhD at the Ohio State University under the direction of Professor Barbara Lee Keyfitz. My research focusses on Mathematical Biology using Differential Equation and Dynamical System approaches. By building new techniques in the Geometric Singular Perturbation Theory, my recent works uncovered mysteries in eco-evolutionary dynamics, epidemic models and predator-prey systems.

Contact

Email: hsut1@math.miami.edu

Publications

• 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)