4 papers
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…
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…
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…