论文标题
团体羊群中的紧急行为
Emergent behaviors in group ring flocks
论文作者
论文摘要
我们在组环上提出了一个一阶聚集模型，并研究其渐近动力学。在正耦合强度状态下，我们表明，所提出的模型产生的流量倾向于渐近平衡歧管。为此，我们引入了一种lyapunov函数，该功能是沿流动的非进攻，并使用非线性函数和LaSalle不变性原理的时间衰变，我们表明该流量是渐近的平衡歧管。我们还表明，平衡歧管的结构在很大程度上取决于基础群体的结构。
We present a first-order aggregation model on a group ring, and study its asymptotic dynamics. In a positive coupling strength regime, we show that the flow generated by the proposed model tends to an equilibrium manifold asymptotically. For this, we introduce a Lyapunov functional which is non-increasing along the flow, and using the temporal decay of the nonlinear functional and the LaSalle invariance principle, we show that the flow converges toward an equilibrium manifold asymptotically. We also show that the structure of an equilibrium manifold is strongly dependent on the structure of an underlying group.
