论文标题
在Hegselmann-Krause模型中具有有限信息速度的Hegselmann-Krause模型中的良好姿势和渐近共识
Well posedness and asymptotic consensus in the Hegselmann-Krause model with finite speed of information propagation
论文作者
论文摘要
我们考虑了共识形成的Hegselmann-Krause模型的变体，其中代理之间的信息以有限的速度$ \ mathfrak {C} $传播。这导致了具有状态依赖性延迟的普通微分方程（ODE）系统。观察到ODE系统的经典体系理论不适用，我们提供了全球存在和模型解决方案独特性的证明。我们证明，只要代理商的旅行速度慢于$ \ Mathfrak {c} $，始终可以在模型的空间一维设置中达成渐近共识。我们还为在空间多维环境中的渐近共识提供了足够的条件。
We consider a variant of the Hegselmann-Krause model of consensus formation where information between agents propagates with a finite speed $\mathfrak{c}$. This leads to a system of ordinary differential equations (ODE) with state-dependent delay. Observing that the classical well-posedness theory for ODE systems does not apply, we provide a proof of global existence and uniqueness of solutions of the model. We prove that asymptotic consensus is always reached in the spatially one-dimensional setting of the model, as long as agents travel slower than $\mathfrak{c}$. We also provide sufficient conditions for asymptotic consensus in the spatially multi-dimensional setting.
