Applied & Computational Mathematics seminar: Self-organized sacrifice: the death of vegetation patches during dry spells

Speaker: Arnd Scheel, University of Minnesota

Title:  Self-organized sacrifice: the death of vegetation patches during dry spells

Abstract:  In ecosystems that cannot sustain dense uniform vegetation, patterns of concentrated vegetation emerge to leverage benefits of dense growth and economize overall resources. As environmental conditions change, such patterns adapt by varying the spacing between and number of vegetated regions. In a prototypical model for pattern formation, the complex Ginzburg-Landau equation, we study the dynamics of wavenumbers in spatially periodic solutions. As parameters slowly pass through an Eckhaus instability, patterns with higher wavenumber become unstable. We predict the resulting drop in wavenumber and the time delay of this transition based on spatio-temporal resonances. I'll also mention work that takes a spatial-temporal gradient rather than just a temporal gradient of the parameter into account.  Based on joint work with Anna Asch, Montie Avery, and Anthony Cortez, and with Ryan Goh and Tasso Kaper 

Time:  Friday, February 23, 2024 - 1:30pm-2:30pm

Place:  Exploratory Hall, room 4106