School of Mathematics
University of Minnesota
NASA Earth

Minnesota Mathematics of Climate Seminar

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Coming Attractions

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.

Time and Location

The meetings are held in 570 Vincent Hall at 11:15 am Central Time on Tuesdays, followed by an extended discussion over lunch at the Bona Restaurant. If you would like to participate remotely, please contact Richard McGehee <>.


Richard McGehee, School of Mathematics, <>
Clarence Lehman, College of Biological Sciences, <>


This seminar examines some of the simpler mathematical models of climate in the recent literature. Participants are encouraged to read a paper and report on it to the other participants, but passive participation is also welcomed. Course credit can be arranged either through the School of Mathematics or the Department of Ecology, Evolution and Behavior by arrangement with the organizers.

Last update: February 26, 2023
©2023 Richard McGehee