论文标题
与分布式反应延迟的cucker-smale模型中的指数渐近羊
Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays
论文作者
论文摘要
我们研究具有分布式反应延迟的cucker-smale系统的变体。使用二次速度波动上的向后和稳定性估计，我们为溶液的渐近羊群提供了足够的条件。条件是根据延迟分布的矩制定的，并保证了速度波动的指数衰减，以在大时向零时零。我们证明了理论对特定延迟分布的适用性 - 指数，统一和线性。对于指数分布，可以通过分析解决羊群条件，从而导致明确的公式。对于其他两个分布，对假设的满意度进行了数值研究。
We study a variant of the Cucker-Smale system with distributed reaction delays. Using backward-forward and stability estimates on the quadratic velocity fluctuations we derive sufficient conditions for asymptotic flocking of the solutions. The conditions are formulated in terms of moments of the delay distribution and they guarantee exponential decay of velocity fluctuations towards zero for large times. We demonstrate the applicability of our theory to particular delay distributions - exponential, uniform and linear. For the exponential distribution, the flocking condition can be resolved analytically, leading to an explicit formula. For the other two distributions, the satisfiability of the assumptions is investigated numerically.
