论文标题
在Hegselmann-Krause模型中具有传输型延迟的直接证明无条件渐近共识
Direct proof of unconditional asymptotic consensus in the Hegselmann-Krause model with transmission-type delay
论文作者
论文摘要
我们提供了具有传输类型延迟的非线性Hegselmann-Krause模型中渐近共识的直接证明，其中通信权重取决于相空间中的粒子距离。我们的方法基于对群体直径在有限时间间隔内收缩的明确估计，并避免使用Lyapunov型功能或非负矩阵理论的结果。它适用于模型的原始配方，其通信权重缩放为代理的数量，并随着权重标准化了A'la Motsch-Tadmor。我们仅对模型参数提出最小的假设。特别是，我们仅假定影响功能的全球积极性，而不会对其衰减率或单调性施加任何条件。此外，我们的结果适用于任何延迟的任何长度。
We present a direct proof of asymptotic consensus in the nonlinear Hegselmann-Krause model with transmission-type delay, where the communication weights depend on the particle distance in phase space. Our approach is based on an explicit estimate of the shrinkage of the group diameter on finite time intervals and avoids the usage of Lyapunov-type functionals or results from nonnegative matrix theory. It works for both the original formulation of the model with communication weights scaled by the number of agents, and the modification with weights normalized a'la Motsch-Tadmor. We pose only minimal assumptions on the model parameters. In particular, we only assume global positivity of the influence function, without imposing any conditions on its decay rate or monotonicity. Moreover, our result holds for any length of the delay.
