Titlebook: Dynamics and Analysis of Alignment Models of Collective Behavior; Roman Shvydkoy Book 2021 Springer Nature Switzerland AG 2021 Cucker-Smal

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978-3-030-68146-3Springer Nature Switzerland AG 2021

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Roman ShvydkoyIntroduces a special class of alignment model called the Cucker-Smale system as well as its kinetic and hydrodynamic counterparts.Presents cutting-edge research in the area of collective behavior, inc

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Infinitesimal

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One-Dimensional Theory,The underlying theme will be to relate regularity and flocking behavior of the system to a new conserved quantity which is available in dimension 1 and for a few other exceptional multi-dimensional solutions. We highlight its analytical and physical roles in the alignment dynamics.

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https://doi.org/10.1007/978-3-86226-841-2nimal behavior distinguish three basic regions of mutual interactions between agents—repulsion, alignment, and attraction. More refined modeling such as inclusion of cones of vision into the alignment zone, nearest neighbor rule, self-propulsion, friction, noise, and external confinement allow to re

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https://doi.org/10.1007/978-3-86226-841-2esponding kinetic formulation and its variants can be derived formally via the BBGKY hierarchy. We will present a rigorous derivation of the Vlasov-type kinetic model via the mean-field limit and along the way establish contractivity and asymptotic stability estimates for solutions. Many of the coll

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