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Characterizing High-dimensional Dynamics by Combinatorial-Topological Methods on a Latent Space
Patrick Bailon, Marcio Gameiro, Brittany Gelb +5
Combinatorial-topological methods for characterizing dynamics are rigorous, generalizable, computable, and they only require approximations, but the dimension of the phase space is…
Compositionality of Global Dynamics in Product and Skew-Product Systems
William D. Kalies, Tony Wehbe
We study the compositionality of global dynamics through attractor lattices and order structures of recurrent dynamics in product and skew-product systems using Conley theory. For…
Conley Index Theory for Hybrid Systems
Bernardo Rivas, William Kalies
We define a homological Conley index for a class of hybrid dynamical systems. This is achieved by factoring through the hybrid suspension semiflow, which views a class of hybrid dy…
Topological Dynamics via Learned Hybrid Systems
Bernardo Rivas, Kaito Iwasaki, William Kalies +2
The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid s…
Data-driven Identification of Attractors Using Machine Learning
Marcio Gameiro, Brittany Gelb, William Kalies +3
In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on…
Priestley duality and representations of recurrent dynamics
William Kalies, Robert Vandervorst
For an arbitrary dynamical system there is a strong relationship between global dynamics and the order structure of an appropriately constructed Priestley space. This connection pr…