Minnesota Mathematics of Climate Seminar

Attractors of Nonsmooth and Multivalued Dynamical Systems with an Application in Oceanography

Cameron Thieme

Center for Discrete Mathematics and Theoretical Computer Science, Rutgers University

11:15 am CST, Tuesday, February 28, 2023

570 Vincent Hall (also streamed via Zoom)

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; we will study one such model--Welander's ocean box model--as an example throughout this talk. These nonsmooth systems are typically reframed as Filippov systems or differential inclusions, 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.