论文标题
球体上的cucker-smale型羊群模型
Cucker-Smale type flocking models on a sphere
论文作者
论文摘要
我们在球体上提出了一个Cucker-Smale（C-S）型羊群。我们研究球体上的速度比对，并证明了该模型的羊群的出现。我们的模型包括三个新术语：中心力，球体上的多代理相互作用和颗粒间键合力。为了比较不同切线空间上的速度向量，我们在新的相互作用项中介绍了一个旋转操作员。由于几何限制，旋转算子在抗虫点处是单数，并且位于这些点处的两个试剂之间的相对速度没有明确定义。基于我们模型的能量耗散特性和Barbalat引理的变化，我们显示了可接受的通信权重功能类别的速度对齐。此外，对于足够大的键合力，我们证明了时间 - 肿瘤，其中包括避免对抗点。
We present a Cucker-Smale (C-S) type flocking model on a sphere. We study velocity alignment on a sphere and prove the emergence of flocking for the proposed model. Our model includes three new terms: a centripetal force, multi-agent interactions on a sphere and inter-particle bonding forces. To compare velocity vectors on different tangent spaces, we introduce a rotation operator in our new interaction term. Due to the geometric restriction, the rotation operator is singular at antipodal points and the relative velocity between two agents located at these points is not well-defined. Based on an energy dissipation property of our model and a variation of Barbalat's lemma, we show the alignment of velocities for an admissible class of communication weight functions. In addition, for sufficiently large bonding forces we prove time-asymptotic flocking which includes the avoidance of antipodal points.
