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 …

We study emergent collective behaviors of a thermodynamic Cucker-Smale (TCS) ensemble
on complete smooth Riemannian manifolds. For this, we extend the TCS model on the …

We study the mean-field limit of the Cucker-Smale (CS) model for flocking on complete
smooth Riemannian manifolds. For this, we first formally derive the kinetic manifold CS …

We study the approximation of the nonlocal-interaction equation restricted to a compact
manifold $\mathcal {M} $ embedded in $\mathbb {R}^ d $, and more generally compact sets …

We derive an explicit form for the Cucker--Smale (CS) model on the special orthogonal
group SO(3) by identifying closed form expressions for geometric quantities such as …

We investigate a model for collective behaviour with intrinsic interactions on smooth
Riemannian manifolds. For regular interaction potentials, we establish the local well …

We consider a model for collective behaviour on Riemannian manifolds, with interactions
modelled through a smooth interaction potential that depends on the squared intrinsic …

We consider a spatially homogeneous Kolmogorov–Vicsek model in two dimensions, which
describes the alignment dynamics of self-driven stochastic particles that move on a plane at …

We investigate the long-time behaviour of solutions to a nonlocal partial differential equation
on smooth Riemannian manifolds of bounded sectional curvature. The equation models self …

We study an intrinsic model for collective behaviour on the hyperbolic space H n. We
investigate the equilibria of the aggregation equation (or equivalently, the critical points of …