Stroboscopic and Poincaré Maps - Data-Driven Dynamics | Lecture 9

In this lecture we demonstrate an application of the SINDy method to stroboscopic and Poincaré maps. Through this exploration we show that SINDy can not only be used to discover new ODEs from data, but can be used to analyze the systems we already have. This lecture features both theoretical discussions along with two coding demonstrations that highlight both the choice of the SINDy dictionary and the choice of the sparsity parameter. Learn more about the theoretical side of Poincaré maps here: https://www.youtube.com/watch?v=-TgvrZ_sQLs&t=4s My own work on using SINDy to discover mappings: https://www.sciencedirect.com/science/article/abs/pii/S0167278919305470 Coding demonstration in MATLAB comes from SINDy_map.m here: https://github.com/jbramburger/DataDrivenDynSyst/tree/main/Identifying%20Nonlinear%20Dynamics Get the book here: https://epubs.siam.org/doi/10.1137/1.9781611978162 Scripts and notebooks to reproduce all examples: https://github.com/jbramburger/DataDrivenDynSyst This book provides readers with: - methods not found in other texts as well as novel ones developed just for this book; - an example-driven presentation that provides background material and descriptions of methods without getting bogged down in technicalities; - examples that demonstrate the applicability of a method and introduce the features and drawbacks of their application; and - a code repository in the online supplementary material that can be used to reproduce every example and that can be repurposed to fit a variety of applications not found in the book. More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.