具有生物记忆项的粒子与动力学系统中的渐近群聚行为
Asymptotic Flocking Behavior in Particle and Kinetic Systems with biological Memory Term
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中文总结 AI 辅助
该研究探讨带生物记忆项的Cucker-Smale型群聚模型，发现记忆会增加群聚难度，明确了微观与介观层面实现群聚的条件及通信强度范围的变化。
中文摘要 AI 辅助
我们研究了带有生物记忆项的Cucker-Smale型群聚模型，得出记忆会使群聚更难实现的结论。该模型引入$h(t)$描述记忆，其动力学方程$\frac{dh}{dt}=x(t)+v(t)-\beta h(t)$反映了路径、速度依赖与指数衰减特性。在微观层面，群聚现象呈条件性，要求通信核$\beta(t)$具有多项式下界且记忆偏差$H(t)$指数衰减；在介观层面，群聚速率呈指数或代数衰减，通信强度$\beta$的适用范围更小。
英文摘要
We investigate a Cucker-Smale type flocking model with a biological memory term and conclude that memory makes flocking harder. The model introduces $h(t)$ to describe memory, with dynamics $\frac{dh}{dt}=x(t)+v(t)-λh(t)$ reflecting path, velocity dependence and exponential decay. In microscopic level, the flocking phenomenon becomes conditional, requires communication kernel $ψ(t)$ has polynomial lower bound and memory deviation $H(t)$ decays exponentially. In mesoscopic level, flocking rates exhibit exponential or algebraic decay and the range of communication strength $β$ become smaller.
