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Roman Shvydkoy, RLM 10.176: Dynamics of emergence: from Cucker-Smale to topological models
Wednesday, February 20, 2019, 01:00pm - 02:00pm
In this talk we will discuss a new class of flocking models thatappear in various biological systems exhibiting swarming self-organizedbehavior. Since the introduction of Cucker-Smale systems, thatare designed to describe basic flocking dynamics, the analysisof long time behavior relied on sufficiently strong long rangeinteractions. The main feature of the new class is emergenceof global alignment with only local communication present betweenclosest neighbors. A series of new structural components hadto be introduced to achieve this, including use of singular kernels,and topological adaptive diffusion that enhances alignment mechanism.The resulting systems are of fractional parabolic type with roughdrift and force, which present many challenges form the pointof view of analysis. We will present new global well-posednessand long time behavior results for these systems.
Location: RLM 10.176

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