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TITLE Emergent Behaviors of Cucker-Smale Flocks on Riemannian Manifolds
KIAS AUTHORS Kim, Doheon,Ha, Seung-Yeal
JOURNAL IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2021
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ABSTRACT In this article, we present a new Cucker-Smale model on smooth Riemannian manifolds using the concepts of covariant derivative and parallel transport, and we also study its emergent dynamics under an a priori assumption on the energy functional. For Euclidean space, our proposed model coincides with the original Cucker-Smale model. As concrete examples, we consider three Riemannian manifolds: the unit 2-sphere, the unit circle, and the Poincare half-plane, and provide explicit reductions from the proposed general model to aforementioned manifolds via explicit formulas for the covariant derivative and parallel transport.
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