The "Nonlinear Waves and Coherent Structures Online Colloquium" is a monthly seminar that will have speakers from a diverse range of disciplines to speak on a broad range of topics connected to nonlinear waves and coherent structures. The organizers hope this series will help maintain a sense of community and provide a broad audience with access to research developments on the forefront of this field.
NWCS Colloquium
Jason Bramburger (Department of Mathematics and Statistics, Concordia University)
Title: Pattern formation, persistence, and stability over random networks
Abstract: This talk overviews my recent work on understanding pattern formation, persistence, and stability in dynamical systems posed on large random networks using graphons as continuum limits. I will show how graphon Laplacians provide a tractable framework for analyzing Turing type instabilities and pattern forming bifurcations in random networks, yielding rigorous connections between continuum spectra and bifurcations observed in finite graphs with high probability. I will then discuss persistence results demonstrating that non-degenerate steady-states of graphon dynamical systems and their linear stability properties persist in sufficiently large random network realizations. Finally, I will highlight recent results on synchronization in random oscillator networks, where a graphon formulation of the Kuramoto model identifies critical coupling thresholds and bifurcations to synchronized states that accurately predict behaviour in large finite networks.
How to join: An email containing the zoom link and password for the seminar will be sent out by 9:30am (Eastern Time) the day of the talk. To join the email list please register here
Speakers: To see the full list of upcoming speakers and recordings of prior talks, click here
Organizers:
Stathis Charalampidis, SDSU, San Diego
Sathyanarayanan Chandramouli, UMass Amherst
Panos Kevrekidis, UMass Amherst