Mathematics Colloquia and Seminars

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Description

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.