时滞耦合群体中的不稳定振荡和双稳定性
Unstable oscillations and bistability in delay-coupled swarms
摘要：
从理论和实验两方面都知道，将时间延迟引入到移动代理群的通信网络中会产生相干的旋转模式。通常，这种时空旋转可以与其他群集模式（如铣削和植绒）相结合。然而，大多数已知的延迟耦合群相关的分歧结果依赖于不准确的平均场技术。因此，应用宏观理论作为预测和控制移动机器人群的指导的效用已经受到限制。为了克服这一限制，我们进行了一个精确的稳定性分析的两个主要的群集模式在一个一般的模型与时间延迟的相互作用。通过正确识别在存在时间延迟的情况下确定稳定性的相关时空模式，我们能够准确地预测大型群模拟中的双稳态和不稳定振荡-为与机器人实验进行比较奠定了基础。
英文摘要：
It is known from both theory and experiments that introducing time delays into the communication network of mobile-agent swarms produces coherent rotational patterns. Often such spatio-temporal rotations can be bistable with other swarming patterns, such as milling and flocking. Yet, most known bifurcation results related to delay-coupled swarms rely on inaccurate mean-field techniques. As a consequence, the utility of applying macroscopic theory as a guide for predicting and controlling swarms of mobile robots has been limited. To overcome this limitation, we perform an exact stability analysis of two primary swarming patterns in a general model with time-delayed interactions. By correctly identifying the relevant spatio-temporal modes that determine stability in the presence of time delay, we are able to accurately predict bistability and unstable oscillations in large swarm simulations-- laying the groundwork for comparisons to robotics experiments.
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