Controlled pattern formation of stochastic Cucker–Smale systems with network structures

Young Pil Choi; Doeun Oh; Oliver Tse

doi:10.1016/j.cnsns.2022.106474

Controlled pattern formation of stochastic Cucker–Smale systems with network structures

Young Pil Choi, Doeun Oh, Oliver Tse

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present a new stochastic particle system on networks which exhibits flocking behavior and pattern formation. More precisely, we consider Cucker–Smale particles with decentralized formation control and multiplicative noises on symmetric connected networks. Under suitable assumptions on the initial configurations and the network structure, we establish time-asymptotic stochastic flocking behavior and pattern formation of solutions for the proposed stochastic particle system. Our approach is based on the Lyapunov functional energy estimates and does not require any spectral information of the graph associated with the network structure.

Original language	English
Article number	106474
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	111
DOIs	https://doi.org/10.1016/j.cnsns.2022.106474
Publication status	Published - 2022 Aug

Bibliographical note

Funding Information:
YPC acknowledges support from NRF, South Korea grant (No. 2017R1C1B2012918 ), POSCO Science Fellowship of POSCO TJ Park Foundation , and Yonsei University Research Fund of 2019-22-0212 and 2020-22-0505 . OT acknowledges support from NWO Vidi grant 016.Vidi.189.102, “Dynamical-Variational Transport Costs and Application to Variational Evolutions”.

Publisher Copyright:
© 2022 Elsevier B.V.

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modelling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2022.106474

Cite this

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title = "Controlled pattern formation of stochastic Cucker–Smale systems with network structures",

abstract = "We present a new stochastic particle system on networks which exhibits flocking behavior and pattern formation. More precisely, we consider Cucker–Smale particles with decentralized formation control and multiplicative noises on symmetric connected networks. Under suitable assumptions on the initial configurations and the network structure, we establish time-asymptotic stochastic flocking behavior and pattern formation of solutions for the proposed stochastic particle system. Our approach is based on the Lyapunov functional energy estimates and does not require any spectral information of the graph associated with the network structure.",

author = "Choi, {Young Pil} and Doeun Oh and Oliver Tse",

note = "Funding Information: YPC acknowledges support from NRF, South Korea grant (No. 2017R1C1B2012918 ), POSCO Science Fellowship of POSCO TJ Park Foundation , and Yonsei University Research Fund of 2019-22-0212 and 2020-22-0505 . OT acknowledges support from NWO Vidi grant 016.Vidi.189.102, “Dynamical-Variational Transport Costs and Application to Variational Evolutions”. Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2022",

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doi = "10.1016/j.cnsns.2022.106474",

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T1 - Controlled pattern formation of stochastic Cucker–Smale systems with network structures

AU - Choi, Young Pil

AU - Oh, Doeun

AU - Tse, Oliver

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PY - 2022/8

Y1 - 2022/8

N2 - We present a new stochastic particle system on networks which exhibits flocking behavior and pattern formation. More precisely, we consider Cucker–Smale particles with decentralized formation control and multiplicative noises on symmetric connected networks. Under suitable assumptions on the initial configurations and the network structure, we establish time-asymptotic stochastic flocking behavior and pattern formation of solutions for the proposed stochastic particle system. Our approach is based on the Lyapunov functional energy estimates and does not require any spectral information of the graph associated with the network structure.

AB - We present a new stochastic particle system on networks which exhibits flocking behavior and pattern formation. More precisely, we consider Cucker–Smale particles with decentralized formation control and multiplicative noises on symmetric connected networks. Under suitable assumptions on the initial configurations and the network structure, we establish time-asymptotic stochastic flocking behavior and pattern formation of solutions for the proposed stochastic particle system. Our approach is based on the Lyapunov functional energy estimates and does not require any spectral information of the graph associated with the network structure.

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Controlled pattern formation of stochastic Cucker–Smale systems with network structures

Abstract

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