Electron. J. Differential Equations, Vol. 2021 (2021), No. 104, pp. 1-24.
Dynamics of flocking models with two species
Qingjian Zhao, Shaoyun Shi, Wenlei Li
Abstract:
This article studies the flocking behavior of self-organized agents in two species.
First, referring to the work of Olfati-Saber and the classical Cucker-Smale model,
we establish a discrete system describing the flocking dynamic of the agents in two species.
Second, by using the LaSalle's invariance principle, we show that the system with
global interaction will achieve unconditional time-asymptotic flocking, and the
system with local interaction has a time-asymptotic flocking under certain assumptions.
Moreover, we investigate the local asymptotic stability of a class of flocking solutions.
Finally, some numerical simulations and qualitative results are presented.
Submitted August 14, 2021. Published December 30, 2021.
Math Subject Classifications: 34D20, 92D25, 37D10, 65L07.
Key Words: Flocking dynamics; discrete model, LaSalle invariance principle; invariant manifold.
DOI: https://doi.org/10.58997/ejde.2021.104
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Qingjian Zhao
School of Mathematics
Jilin University
Changchun 130012, China
email: zhaoqj17@mails.jlu.edu.cn
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Shaoyun Shi
School of Mathematics & State key laboratory of automotive
simulation and control
Jilin University
Changchun 130012, China
email: shisy@jlu.edu.cn
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Wenlei Li
School of Mathematics
Jilin University
Changchun 130012, China
email: lwlei@jlu.edu.cn
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