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DTSTART:20070311T020000
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DTSTAMP:20230922T154703
DTSTART;TZID=America/Detroit:20231114T160000
DTEND;TZID=America/Detroit:20231114T170000
SUMMARY:Workshop / Seminar:The Van Eenam Lecture I: Mean Field Games and Kuramoto Synchronization
DESCRIPTION:Abstract: Main goal of this talk is to introduce an exciting new area of mean field games modeling interactions between large number of identical particles. In this formalism\, instead of positing the dynamics of the individual particles\, one lets them endogenously determine their behaviors by minimizing a given cost functional and hopefully\, settling in a Nash equilibrium. Initiated by Larry & Lions\, and Huang\, Malhame\, & Caines in 2006\, mean field games has found an amazing range of applications.  This talk uses the specific example of classical Kuromato synchronization to introduce the novel approach and its potential.  Originally motivated by systems of chemical  and biological oscillators\, the Kuramoto system is the key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior  of the system. While the system is unsynchronized when this term is not sufficiently strong\, fascinatingly\, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter.  Mean field approach also delivers same type of results including the phase transition from incoherence to synchronization.
UID:101812-21816433@events.umich.edu
URL:https://events.umich.edu/event/101812
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:AEM Featured,Mathematics
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