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논문

Asymptotic dynamics for the Cucker?Smale-type model with the Rayleigh friction

https://doi.org/10.1088/1751-8113/43/31/315201

  • 저자Seung-Yeal Ha, Taeyoung Ha, Jong-Ho Kim
  • 학술지Journal of Physics A: Mathematical and Theoretical 43
  • 등재유형
  • 게재일자(2010)


We study the asymptotic flocking dynamics for the Cucker–Smale-type second-order continuous-time dynamical system with the Rayleigh friction. For mean-field communications with a positive lower bound, we show that an asymptotic flocking occurs for any compactly supported initial configuration in a large coupling regime. In contrast, in a small coupling regime, an asymptotic flocking is possible for a restricted class of initial configurations near complete flocking states. We also present several numerical simulations and compare them with our analytical results.


We study the asymptotic flocking dynamics for the Cucker–Smale-type second-order continuous-time dynamical system with the Rayleigh friction. For mean-field communications with a positive lower bound, we show that an asymptotic flocking occurs for any compactly supported initial configuration in a large coupling regime. In contrast, in a small coupling regime, an asymptotic flocking is possible for a restricted class of initial configurations near complete flocking states. We also present several numerical simulations and compare them with our analytical results.

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