Exploring high-dimensional dynamical systems
From pendulums to planets, dynamical systems are everywhere. We understand them the best when the dimension of the system is either low or infinite, while those in the middle (with dozens or hundreds of degrees of freedom) pose a unique challenge. In this talk, I will explore dynamical systems with high but finite dimensions, especially when they can be represented by networks of coupled oscillators. Because the network naturally partitions the system into subsystems (i.e., nodes), we can meaningfully study their collective dynamics, such as synchronization; we can also utilize the structure encoded in the network to perform dimension reduction. Throughout the talk, I will discuss mathematical techniques for analyzing these high-dimensional systems, the emergent properties they reveal, and the potential lessons they teach us about systems such as circadian clocks and artificial neural networks.
For those that will be unable to attend this talk in person, a Zoom link is also available: https://illinois.zoom.us/j/84609122633?pwd=dzhsajhZNFlNWWlGcit6TzJBc1RtQT09
