Multi-cluster Dynamics Behaviors of Cucker-Smale Model Involving Unit-Speed Constraint and State-Dependent Delay

Abstract

As the time lag of information exchange between individuals depends on the relative position and density, state-dependent delay would be involved in the models of collective behaviors, naturally. In this paper, we focus on the influences of state-dependent delay on the multi-cluster behavior for a Cucker-Smale model with unit-speed constraint. Considering the state-dependent delay system, we prove the existence and uniqueness of solutions, and show the multi-cluster flocking behavior. Furthermore, we present an estimation of the critical coupling strength and a critical information propagation speed. Finally, we provide numerical simulations for different coupling strengths to discuss the number of clusters.

Keywords

Cucker-Smale model / Unit-speed constraint / State-dependent delay / Multi-cluster / 34K20 / 34K60 / 82C22 / 92D50

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Funding

National Natural Science Foundation of China(12371180)

Instituto Nacional de Ciência e Tecnologia Centro de Estudos das Adaptações da Biota Aquática da Amazônia(XJJC2024057)

RIGHTS & PERMISSIONS

Shanghai University

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