具有空间坐标耦合的二阶集群模型分析

在空间坐标耦合的情形下建立一种改进的二阶分布式集群模型。分析结果显示,如果系统的拓扑结构不变,当其确定的有向图具有有向支撑树并且速度的伴随系数大于某一临界值时,整个群体将随着耦合矩阵的旋转角的变化而呈现出三种集群样式——直线模式、圆柱螺线模式以及对数螺线模式。最后给出了这三种样式所对应的数值仿真结果。

Analysis for second-order collective model with spatial coordinate coupling

In this paper, a second-order distributed collective model with spatial coordinates coupling is established. If the topology structure of the system is unchanged, the system graph has a directed spanning tree and the speed parameter is over the critical value, then the system comes three flocking patterns: when the rotation angle is under the critical value, the collective system converges to a linear pattern; when the angle equal to the critical value, the collective system converges to a cylindrical spiral pattern; and when the rotation angle is over the critical value, the collective system converges to a logarithmic spiral pattern. Some simulations are considered in the last section.