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Flocking and pattern motion in a modified Cucker-Smale model

机译:改良的Cucker-Smale模型中的植绒和图案运动

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Self-organizing systems arise very naturally in artificial intelligence, and in physical, biological and social sciences. In this paper, we modify the classic Cucker-Smale model at both microscopic and macroscopic levels by taking the target motion pattern driving forces into consideration. Such target motion pattern driving force functions are properly defined for the line-shaped motion pattern and the ball-shaped motion pattern. For the modified Cucker-Smale model with the prescribed line-shaped motion pattern, we have analytically shown that there is a flocking pattern with an asymptotic flocking velocity. This is illustrated by numerical simulations using both symmetric and non-symmetric pairwise influence functions. For the modified Cucker-Smale model with the prescribed ball-shaped motion pattern, our simulations suggest that the solution also converges to the prescribed motion pattern.
机译:自组织系统在人工智能以及物理,生物和社会科学中非常自然地出现。在本文中,我们通过考虑目标运动模式驱动力,从微观和宏观两个层面修改了经典的Cucker-Smale模型。对于线形运动图案和球形运动图案适当地定义了这种目标运动图案驱动力函数。对于具有规定的线形运动模式的改进的Cucker-Smale模型,我们已分析地表明存在一种具有渐近植绒速度的植绒模式。这通过使用对称和非对称成对影响函数的数值模拟来说明。对于具有规定球形运动模式的改进的Cucker-Smale模型,我们的仿真表明,该解也收敛于规定运动模式。

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