We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatio-temporal scales of the swarm structures, and also demonstrate how the complicated interplay of coupling strength, time delay, noise intensity, and choice of initial conditions can affect the swarm. In particular, our studies show that for sufficiently large values of the coupling strength and/or the time delay, there is a noise intensity threshold that forces a transition of the swarm from a misaligned state into an aligned state. We show that this alignment transition exhibits hysteresis when the noise intensity is taken to be time dependent.
Chimera states in complex networks: interplay of fractal topology and delay
嵌合体状态是在相同振荡器网络中出现的有趣的部分同步模式的一个例子。它们包括空间共存的域的相干（同步）和非相干（去相干化）的动态。我们分析了具有层次连接性的Van der Pol振子网络中的嵌合态，并详细阐述了耦合项中引入的时滞的作用。在耦合强度和延迟时间的参数平面中，我们发现了嵌合体状态存在的舌状区域与相干行波存在的区域交替。我们证明，通过改变时间延迟，可以故意稳定所需的时空模式的系统。
