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CCMS Colloquium: Mary Lou Zeeman (Bowdoin College)
February 20 @ 11:00 am - 12:15 pm
CCMS Colloquium invites you to a talk by Mary Lou Zeeman (Bowdoin College)
Title: A new framework for studying transient reactivity in two-dimensional systems.
Abstract: Even if a linear system of ordinary differential equations (ODEs) has a globally attracting equilibrium, solutions of the ODEs may grow arbitrarily large in the short-term before returning to the equilibrium in the long-term. This counter-intuitive phenomenon of transient amplification is called reactivity. It is especially important in ecological resilience and other applications where disturbances of a system may be transiently magnified to undesirable levels. In this talk we introduce a new framework for analyzing reactivity in two-dimensional linear systems of ODEs. While the eigenstructure of the system captures the long-term dynamics, we use the new framework to define an orthostructure, dual to the eigenstructure, that captures transient reactivity dynamics of the system. By interweaving the eigen- and ortho-structures, we are able to exactly quantify the maximum disturbance amplification possible.
Bio: Mary Lou Zeeman is the Wells Johnson Professor of Mathematics at Bowdoin College. Her research is in dynamical systems with applications to biology, sustainability and resilience. She is known for collaboratively building cross-disciplinary research communities focused on the health of the planet. She helped found and co-lead the Mathematics and Climate Research Network, the Computational Sustainability Network and the SIAM Activity Group on Mathematics of Planet Earth.
