自推进群体中的时滞诱导不稳定性
Delay Induced Instabilities in Self-Propelling Swarms
摘要：
考虑了在噪声和通信时延存在的情况下，自推进粒子通过两两吸引力相互作用的一般模型。Erdmann等人先前的工作[Phys. Rev. E { \bf 71}，051904（2205）]已经表明，足够大的噪声强度将导致个体的平移群转变为具有固定质心的旋转群。我们表明，随着时间延迟的增加，该模型具有依赖于耦合振幅的大小的过渡。这种转变是独立的初始群体状态（旅行或旋转），其特征是所有的个人随着群体振荡对齐。通过考虑无噪声的平均场方程，我们证明了时滞诱导的跃迁与一个Hopf分岔相关联。分析结果与数值计算的耦合参数的值在霍普夫点产生良好的协议。
英文摘要：
We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann, et al. [Phys. Rev. E {\bf 71}, 051904 (2205)] has shown that a large enough noise intensity will cause a translating swarm of individuals to transition to a rotating swarm with a stationary center of mass. We show that with the addition of a time delay, the model possesses a transition that depends on the size of the coupling amplitude. This transition is independent of the initial swarm state (traveling or rotating) and is characterized by the alignment of all of the individuals along with a swarm oscillation. By considering the mean field equations without noise, we show that the time delay induced transition is associated with a Hopf bifurcation. The analytical result yields good agreement with numerical computations of the value of the coupling parameter at the Hopf point.
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