Emergent dynamics of the inertial spin model and its generalized models

Thời gian: 9h30, thứ 6 ngày 16/10/2026

Địa điểm: Hội trường Hoàng Tụy, Nhà A6, Viện Toán học

Tóm tắt: In this talk, we discuss recent progress on the flocking estimates for the inertial spin(IS) model on the three-dimensional Euclidean space, and high-dimensional generalization of the three-dimensional one. For two-dimensional case, it reduces to the inertial Kuramoto model for synchronization. For quantitative  flocking estimates, we derive a system of differential inequalities for relative kinetic and spin energies, and explicitly obtain exponential flocking under the proposed frameworks. We also introduce a high-dimensional inertial spin model which generalizes the inertial spin model on three-dimensional Euclidean space and study its emergent behaviors. For the generalization of the IS model to the high-dimensional Euclidean space, we replace the cross product by the multiplication via skew-symmetric matrix, and identify a new set of constants of motions which are conserved along the proposed model. We provide two frameworks leading to the collective behaviors of the high-dimensional IS model leading to qualitative and quantitative emergent dynamics in terms of system parameters and initial data.