Research

Click here for an up-to-date CV.

Mathematical Interests

  • Dynamical systems
  • Nonsmooth dynamics
  • Bifurcation theory
  • Floquet theory
  • Perturbation theory
  • Coupled oscillator theory

Biological Interests

  • Dendritic spines (function and formation)
  • Molecular motor transport
  • Cortical function: auditory processing, oscillations, spatial memory
  • Central pattern generators

In Preparation

  1. Holmlund, V., Bailey-Feliciano, B., Adams, K., Pan, J., Ramirez-Zuniga, I., Park, Y. "The Effects of Hematopoiesis on Chronic Critical Illness Following Sepsis."
  2. Park, Y., Fai, T.G. "Mean First Passage Time of Vesicle Translocation in Dendritic Spines." (2026, submitted)
  3. Wang, J., Park, Y., Morsky, B., "Synchronized Disease and Behavioral Dynamics in Weakly Coupled Populations" (2026, submitted).

Peer-Reviewed Publications

  1. Park, Y., "n:m Phase-Locking of Heterogeneous and Strongly Coupled Oscillators." SIADS(2026, In press). arXivCode
  2. Park, Y., Wilson, D. "N-Body Interactions of Strongly Coupled Oscillators." SIADS 23.2 (2024). LinkarXivCode
  3. Park, Y., Leduc, C., Etienne-Manneville, S., Portet, S. "Models of vimentin organization under actin-driven transport." Physical Review E 107.5 (2023, Editor's Suggestion). LinkarXivCode
  4. Park, Y., Singh, P., Fai, T.G. "Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines." SIAM Journal on Applied Mathematics 82.3 (2022). LinkarXivCode
  5. Fai, T.G., Park, Y. "Global asymptotic stability of an active disassembly model of flagellar length control." Journal of Mathematical Biology 84.8 (2022). LinkarXivCode
  6. Park, Y., Wilson, D. "High-Order Accuracy Computation of Coupling Functions for Strongly Coupled Oscillators." SIAM Journal on Applied Dynamical Systems 20.3 (2021). LinkarXivCode
  7. Park, Y., Fai, T.G. "The Dynamics of Vesicles Driven Into Closed Constrictions." Bulletin of Mathematical Biology 82.141 (2020). LinkarXivCode
  8. Park, Y., Geffen, M.N. "A Circuit Model of Auditory Cortex." PLOS Computational Biology 17.6 (2020). LinkbioRxivCode
  9. Ermentrout, G.B., Park, Y., Wilson, D. "Recent advances in coupled oscillator theory." Philosophical Transactions A 377 (2019). LinkarXivCode
  10. Park, Y., Ermentrout, G.B. "A Multiple Timescales Approach to Bridging Spiking- and Population-level Dynamics." Chaos 28.8 (2018). LinkarXivCode
  11. Park, Y., Ermentrout, G.B. "Scalar Reduction of a Neural Field Model with Spike Frequency Adaptation." SIADS 17.1 (2018). LinkarXivCode
  12. Park, Y., Shaw, K.M., Chiel, H.J., Thomas, P.J. "The Infinitesimal Phase Response Curve of Oscillators in Piecewise Smooth Dynamical Systems." EJAM (2018). LinkarXivCode
  13. Park, Y., Ermentrout, G.B. "Weakly Coupled Oscillators in a Slowly Varying World." Springer Journal of Computational Neuroscience 40.3 (2016). LinkarXivCode
  14. Shaw, K.M., Park, Y-M, Chiel, H.J., Thomas, P.J. "Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit." SIAM Journal on Applied Dynamical Systems 11.1 (2012). LinkarXivCode

Undergraduate Journals

  1. Bailey-Feliciano, B., VanVeckhoven, G.W., Pan, J., Park, Y. "A Mathematical Model of Hematopoiesis in Systemic Infection." UF Journal for Undergraduate Research, (2026). LinkarXivCode
  2. Close, B., Rhodes, J., Silverman, C., Park, Y. "Using Differential Equations to Model Heavy Metal Bioaccumulation as part of SCUDEM IX Challenge." UF Journal for Undergraduate Research, (2025). LinkarXiv

Book Chapters

  1. Park, Y., Heitmann, S., Ermentrout, G.B. "The Utility of Phase Models in Studying Neural Synchronization." Chapter in Computational Models of Brain and Behavior, Wiley-Blackwell (2017), 493–504. LinkarXivCode

Theses

  1. Park, Y., "Dimension Reduction of Neural Models Across Multiple Spatio-temporal Scales" (2018). PhD Thesis, University of Pittsburgh. Advisor: G. Bard Ermentrout. Code
  2. Park, Y., "Infinitesimal Phase Response Curves for Piecewise Smooth Dynamical Systems" (2013). MS Thesis, Case Western Reserve University. Advisor: Peter J. Thomas. LinkCode