论文标题
在Hegselmann-Krause和Cucker-Smale模型中，简单的证据证明了具有重新归一化和延迟的Cucker-Smale模型
A simple proof of asymptotic consensus in the Hegselmann-Krause and Cucker-Smale models with renormalization and delay
论文作者
论文摘要
我们在离散的Hegselmann-Krause模型中提供了一个简单的证明，并在离散的Cucker-Smale模型中植入具有重新归一化和可变延迟的离散模型中。它基于重新归一化的通信权重和毛墙式的不平等现象的凸度。与延迟Hegselmann-Krause模型的先前方法相比，我们方法的主要优点是，它不需要对影响功能的最大时间延迟或初始数据或衰减率进行任何限制。从这个角度来看，结果是最佳的。对于cucker-smale模型，它在无数羊群的状态下提供了类似的结果，并具有足够缓慢的腐烂通信速率，但仍然对最大时间延迟的长度不受任何限制。此外，我们证明该方法可以轻松地扩展到Hegselmann-Krause和Cucker-Smale系统的平均范围限制，并使用适当的稳定性结果对测量值的解决方案进行了适当的稳定性结果。
We present a simple proof of asymptotic consensus in the discrete Hegselmann-Krause model and flocking in the discrete Cucker-Smale model with renormalization and variable delay. It is based on convexity of the renormalized communication weights and a Gronwall-Halanay-type inequality. The main advantage of our method, compared to previous approaches to the delay Hegselmann-Krause model, is that it does not require any restriction on the maximal time delay, or the initial data, or decay rate of the influence function. From this point of view the result is optimal. For the Cucker-Smale model it provides an analogous result in the regime of unconditonal flocking with sufficiently slowly decaying communication rate, but still without any restriction on the length of the maximal time delay. Moreover, we demonstrate that the method can be easily extended to the mean-field limits of both the Hegselmann-Krause and Cucker-Smale systems, using appropriate stability results on the measure-valued solutions.
