ASYMPTOTIC FLOCKING VELOCITY AND POSITION FORMULAS FOR THE DELAYED CUCKER-SMALE MODEL

Fen Nie; Yicheng Liu

doi:10.11948/20190146

2021 Volume 11 Issue 4

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Fen Nie, Yicheng Liu. ASYMPTOTIC FLOCKING VELOCITY AND POSITION FORMULAS FOR THE DELAYED CUCKER-SMALE MODEL[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1678-1690. doi: 10.11948/20190146

Citation:

Fen Nie, Yicheng Liu. ASYMPTOTIC FLOCKING VELOCITY AND POSITION FORMULAS FOR THE DELAYED CUCKER-SMALE MODEL[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1678-1690. doi: 10.11948/20190146

ASYMPTOTIC FLOCKING VELOCITY AND POSITION FORMULAS FOR THE DELAYED CUCKER-SMALE MODEL

Fen Nie¹,
Yicheng Liu^1, ,

1.
College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, China

Corresponding author: Email: liuyc2001@hotmail.com(Y. Liu)
Fund Project: The authors were supported by National Natural Science Foundation of China (11671011)

Abstract

Abstract

The Cucker-Smale (short for C-S) model was modified by introduced multiple time delays, and the flocking characteristics of the processing delay C-S model of systems was obtained. Based on the fixed point theorem, we present the existence and uniqueness of the flocking solution for our delayed C-S model when the influence function has the property of Lipschitz and the initial value satisfies certain conditions. At last, we present the asymptotic flocking velocity and the final relative position between agents of the unique flocking solution for such system.
- C-S model /
- flocking solution /
- delay adaptation /
- flocking velocity formula /
- fixed point
MSC: 93C15, 35D30

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References

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