Speaker: Hyukpyo Hong (University of Wisconsin)
Title: Analyzing long-term behavior of dynamical systems using “easy-to-handle” representations
Zoom Link: https://illinois.zoom.us/j/81250100407?pwd=bnZTWHQwNThmd3NEM2ROUWhRc0cvZz09
Abstract: Long-term behaviors of dynamical systems can be described by steady states in deterministic models and stationary distributions in stochastic models. However, direct calculation of such long-term behavior requires solving a system of finitely (or even infinitely) many algebraic equations. In this talk, we introduce chemical reaction network theory, a combinatorial representation of deterministic and stochastic equations that makes it easier to investigate dynamical systems. Interestingly, graph structures can inform the independence of limiting values of variables from system parameters. In addition, we introduce some examples from the Koopman theory, offering a linear representation – not an approximation – of nonlinear dynamics.
References
1. H Hong, J Kim, MA Al-Radhawi, ED Sontag, and JK Kim, Commun. Biol. (2021) https://doi.org/10.1038/s42003-021-02117-x
2. H Hong, BS Hernandez, J Kim, and JK Kim, SIAM J. Appl. Math. (2023) https://doi.org/10.1137/22M150469X
3. Y Hirono, H Hong, JK Kim, arXiv (2023) https://doi.org/10.48550/arXiv.2302.01270
