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

Young Pil Choi, Doeun Oh, Oliver Tse

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number106474
JournalCommunications in Nonlinear Science and Numerical Simulation
Publication statusPublished - 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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