Cameron Thieme, DIMACS

Abstract

Over the past few decades, piecewise-continuous differential equations have become increasingly popular in scientific models. In particular, conceptual climate models often take this form. These nonsmooth systems are typically reframed as Filippov systems, a special type of multivalued dynamical system. Some qualitative properties of these inclusions have been studied over the last few decades, primarily in the context of control systems. Our interest in these systems is in understanding what behavior identified in the nonsmooth model may be continued to families of smooth differential equations which limit to the Filippov system; determining this information is particularly important in this context because the piecewise-continuous model is frequently considered to be a heuristically understandable approximation of a more realistic smooth system. In this talk we will examine how Conley index theory may be applied to the study of differential inclusions in order to address this goal. In particular, we will discuss how attractor-repeller pairs identified in a Filippov system continue to nearby smooth systems.

Bio: Cameron Thieme is a postdoctoral researcher at DIMACS associated with the DATA-INSPIRE Institute.  His research focuses on the use of topological methods in dynamical systems. In particular, he is interested in how classical methods developed for single-valued dynamical systems (flows, maps) may be generalized to set-valued ones; these modern, multivalued dynamical systems have applications in conceptual modeling and data analysis.  He received his PhD in Mathematics at the University of Minnesota under the supervision of Richard McGehee in 2021. 

Presented Via Zoom: https://rutgers.zoom.us/j/95303667237

Meeting ID: 953 0366 7237

Password: 943503