<p>In the paper, the asymptotic flocking behavior of two types of stochastic Cucker-Smale (C-S) systems is considered. Firstly, we investigate a collective migration model with distributed network, taking into account the target velocity, target position, and interactions among particles. The communication rate in this model is disturbed by Gaussian white noise. Based on Barbalat lemma and stochastic analysis, the flocking behavior of the considered model is obtained. Subsequently, the convergence decay rate of the flocking behavior is derived by constructing the corresponding Lyapunov functional. Additionally, the flocking behavior and collision avoidance of stochastic C-S systems with attraction-repulsion kernels are discussed. By applying the Lyapunov functional, the convergence decay rate of flocking behavior in the stochastic C-S system with attraction kernels is analyzed. Finally, several numerical examples are provided to validate correctness of the method.</p>

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Asymptotic Flocking Analysis of Stochastic Cucker-Smale Systems

  • Ji-zhao Huang,
  • Yan Lv

摘要

In the paper, the asymptotic flocking behavior of two types of stochastic Cucker-Smale (C-S) systems is considered. Firstly, we investigate a collective migration model with distributed network, taking into account the target velocity, target position, and interactions among particles. The communication rate in this model is disturbed by Gaussian white noise. Based on Barbalat lemma and stochastic analysis, the flocking behavior of the considered model is obtained. Subsequently, the convergence decay rate of the flocking behavior is derived by constructing the corresponding Lyapunov functional. Additionally, the flocking behavior and collision avoidance of stochastic C-S systems with attraction-repulsion kernels are discussed. By applying the Lyapunov functional, the convergence decay rate of flocking behavior in the stochastic C-S system with attraction kernels is analyzed. Finally, several numerical examples are provided to validate correctness of the method.