Abstract:We consider systems of N particles interacting on the unit sphere in d-dimensional space with dynamics defined as the gradient flow of rotationally invariant potentials. The Kuramoto model on the sphere is a well-studied example of such a system but allows only pairwise interactions. Using the Kuramoto model as a guide, we construct n-body potentials from products and sums of rotation invariants, namely, bilinear inner products and multilinear determinants, which lead to a wide variety of higher-order systems … Show more
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