论文标题
随机cucker-smale系统在谐波场中的植入和集中行为
Flocking and concentration behavior for the stochastic Cucker-Smale system in a harmonic field
论文作者
论文摘要
我们考虑在谐波电位场中具有乘法噪声的Cucker-Smale系统，并研究谐波电位场的效果。在存在外部电源的情况下，由于对齐机制，限制了谐波电位和乘法噪声，预计该系统几乎肯定会肯定地成为速度植入和空间浓度。通过构建随机Lyapunov功能，我们为随机粒子模型几乎肯定地植入和浓度行为得出了足够的条件，并通过数值验证它。然后，我们讨论平均场Vlasov型动力学模型的植入和浓度行为。此外，提供了从随机模型到动力学的均匀范围估算的均匀平均场极限估计的严格分析。
We consider the Cucker-Smale system with multiplicative noise in a harmonic potential field and investigate the effect of harmonic potential field. In the presence of external potential force, the system is expected to emerge into almost surely velocity flocking and spatial concentration, due to the alignment mechanism, confining harmonic potential field and multiplicative noise. By constructing a stochastic Lyapunov functional, we derive a sufficient condition for the almost surely flocking and concentration behavior for the stochastic particle model, and verify it numerically. Then, we discuss the flocking and concentration behavior for the mean field Vlasov-type kinetic model. Moreover, a rigorous analysis of the uniform mean-field limit estimate for the limit process from the stochastic model to the kinetic one is provided.
