Emergence of complete aggregation in the swarm double hyperbolic sphere model

Thời gian: 14h45-15h15, thứ 5 ngày 16 tháng 4 năm 2026

Địa điểm: Phòng 507 nhà A6, Viện Toán học

Tóm tắt:  We study the emergent collective dynamics of swarm particles on the double hyperbolic sphere. For this, we introduce the swarm double hyperbolic sphere (in short, SDHS) model which corresponds to the weak coupling of two swarm hyperbolic sphere models. For the proposed model, we present several analytical conditions on the structure of natural frequency matrices for complete aggregation in which all relative states tend to zero asymptotically. Moreover, we show that the SDHS model reduces to the swarm double hyperbolic Kuramoto model on the Cartesian product of one-dimensional hyperboloids. In this case, the SDHS model admits the pseudo-gradient flow formulation and together withuniform boundedness estimates, the SDHS flow tends to a unique equilibrium, and the flow is exponentially stable under a suitable set of conditions on initial data and coupling strengths.