Critical exponent for Cucker–Smale model under group-hierarchical multi-leadership. (February 2023)

• Record Type: Journal Article
• Authors: Zeng, Fanqin; Xue, Xiaoping; Zhu, Yuchen
• Is Part Of: Applied mathematics letters. Volume 136(2023)
• Publication Date: 2023-02
• Subjects: Unconditional flocking -- Critical exponent -- Group-hierarchical multi-leadership; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.108452
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we focus on the critical exponent for the Cucker–Smale model in R d ( d ≥ 1 ) under group-hierarchical multi-leadership (GHML) topology. The GHML is an asymmetric topology with a group hierarchical structure and multiple leaders. The exponent β in communication weight function measures the decay rate with respect to the distance of particles. In literature, for d ≥ 2, the critical exponent for unconditional flocking is proven to be 1 / 2 only for symmetric topologies or hierarchical leadership. For general digraphs, the exponent below which the unconditional flocking occurs depends on the digraph and is less than 1 / 2 . In this paper, we prove that the critical exponent is 1 / 2 .