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Research

Mathematical Research Interests: Biological Research Interests:
  • Dynamical systems
  • Nonsmooth dynamics
  • Bifurcation theory
  • Floquet theory
  • Perturbation theory
  • Coupled oscillator theory
  • Dendritic spines (function and formation)
  • Molecular motor transport
  • Cortical function:
    • Auditory processing
    • Oscillations
    • Spatial memory
  • Central pattern generators

In Preparation

  1. Mean First Passage Time of Vesicle Translocation Under Varying Geometries

Peer-Reviewed Publications

  1. Park, Y., "n:m Phase-Locking of Heterogeneous and Strongly Coupled Oscillators." (submitted). Link. arXiv. Code.
  2. Park, Y., Wilson, D., "N-Body Interactions of Strongly Coupled Oscillators." SIADS, 23.2 (2024). Link. arXiv. Code.
  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). Link. arXiv. Code.
  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). Link. arXiv. Code.
  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). Link. arXiv. Code.
  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). Link. arXiv. Code.
  7. Park, Y., Fai, T.G., "The Dynamics of Vesicles Driven Into Closed Constrictions." Bulletin of Mathematical Biology, 82.141 (2020). Link. arXiv. Code.
  8. Park, Y., Geffen, M.N., "A Circuit Model of Auditory Cortex." PLOS Computational Biology, 17.6 (2020). Link. bioRxiv. Code.
  9. Ermentrout, G.B., Park, Y., Wilson, D., "Recent advances in coupled oscillator theory." Philosophical Transactions A, 377 (2019). Link. arXiv. Code.
  10. Park, Y., Ermentrout, G.B., "A Multiple Timescales Approach to Bridging Spiking- and Population-level Dynamics." Chaos, 28.8 (2018). Link. arXiv. Code.
  11. Park, Y., Ermentrout, G.B., "Scalar Reduction of a Neural Field Model with Spike Frequency Adaptation." SIADS 17.1 (2018). Link. arXiv. Code.
  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). Link. arXiv. Code.
  13. Park, Y., Ermentrout, G.B., "Weakly Coupled Oscillators in a Slowly Varying World." Springer Journal of Computational Neuroscience, 40.3 (2016). Link. arXiv. Code.
  14. Shaw, K.M., Park, Y-M, Chiel, H.J., and 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). Link. arXiv. Code.

Book Chapters

  1. Park, Y., Heitmann, S. Ermentrout, G.B. "The Utility of Phase Models in Studying Neural Synchronization." Book chapter in "Computational Models of Brain and Behvaior". Wiley-Blackwell 2017, 493-504. Link. arXiv. Code.

Theses