Emergence of bi-cluster flocking for agent-based models with unit speed constraint

Abstract

We study the emergence of bi-cluster flocking for a generalized Justh–Krishnaprasad (J–K) model and the Cucker–Smale (C–S) model with the unit speed constraint. We provide a sufficient framework for the emergence of bi-cluster flocking in terms of initial configurations and communication weights between agents. Our analytical results on bi-cluster flocking illustrate that the spatial-decay rate of communication weights is transferred to the temporal decay rate toward the bi-cluster flocking configuration. We also provide several numerical simulations and compare them to our analytical results.

Emergent Dynamics of the Cucker–Smale Flocking Model and Its Variants

“…In this small coupling strength regime, there might be local flocking(or multi-cluster flocking). Recently this issue has been addressed in a series of papers [16,17,39,40]. [1], C-S model with a singular communication weight is considered.…”

Remarks on the critical coupling strength for the Cucker-Smale model with unit speed

“…For a small coupling strength κ 1, bi-cluster and multi-cluster flockings can emerge from some initial configurations. It has been shown that local flocking, in particular bi-cluster flocking, can emerge from some well-prepared configurations close to bi-cluster configurations [12,13].…”

“…For example, for a long-range communication weight with an infinite L 1 -norm, mono-cluster(global) flocking occurs for any initial configurations. In contrast, for a short-range communication weight, numerical simulations in [12,13] illustrate that mono-cluster(global) flocking does not occur for some initial configurations. There are also interesting works on optimal control of Cucker-Smale model [3,5,7].…”

“…The Cucker-Smale model and its variants have been extensively studied in previous literature [1,2,4,6,8,9,10,12,13,15,16,17,22,24,26,29,30,31,41,42,47] from the viewpoint of mono-cluster flocking in terms of initial configurations and communication weights. For example, for a long-range communication weight with an infinite L 1 -norm, mono-cluster(global) flocking occurs for any initial configurations.…”

Emergent dynamics in the interactions of Cucker-Smale ensembles

“…Recently, in Refs. [9,10], it has been shown that local flocking, in particular bicluster flocking, can emerge from some well-prepared configurations close to bicluster configurations.…”