Analytical aspects of emergent dynamics in systems of collective behavior

Abstract: One of the challenging problems in the field of collective behavior is to understand global emergent phenomena arising from purely local communication between agents. In the context of alignment dynamics examples of such global phenomena include flock formations, reaching consensus of opinions, emergence of leaders, etc. For models based on purely local interactions the assumption of graph-, chain-, or hydrodynamic connectivity of the flock is often necessary, but not always guaranteed, to ensure collective outcome. In this talk we will give an overview of the subject and highlight two new approaches to alignment dynamics in disconnected or weakly connected flocks. One is based on a topological fractional diffusion that resembles the closest neighbor rule originating in various empirical studies, and another based on the use of random fluctuations and the hypocoercivity property for the resulting kinetic Fokker-Planck-Alignment equation.

analysis of PDEs

Audience: researchers in the topic

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Seminar In the Analysis and Methods of PDE (SIAM PDE)

Series comments: The Editorial Board of SIMA and the officers of the SIAM Activity Group on Analysis of Partial Differential Equations (SIAG/APDE) are launching the Seminar In the Analysis and Methods of PDE (SIAM PDE) to be held on the first Thursday of the month at 11:30am ET, except in August and January. The COVID-19 pandemic and consequent social distancing call for online venues of research dissemination. This webinar will serve as a way to recognize achievements in our area, and it will be expected to help promoting the standing of both SIMA and APDE. Further, these webinars should be beneficial to mathematicians who are in relatively isolated places.

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The SIAM PDE Webinar was initiated on June 2020:

By the SIMA Editors:

Robert Lipton, SIMA Editor-in-Chief (Louisiana State University, USA)

Athanasios Tzavaras (KAUST, Saudi Arabia)

By the SIAG/APDE Officers:

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