Mier-Y-Teran-Romero Luis, Forgoston Eric, Schwartz Ira B
Joint NIH postdoctoral fellow with the Johns Hopkins University and the US Naval Research Laboratory, Nonlinear Systems Dynamics Section, Code 6792, Washington, DC 20375, USA.
Rep U S. 2011:3905-3910. doi: 10.1109/IROS.2011.6048160.
We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a translating state and a rotating state with stationary center of mass. Time delayed communication creates a bifurcation pattern dependent on the coupling amplitude between particles. Using a mean field model in the large number limit, we show how the complete bifurcation unfolds in the presence of communication delay and coupling amplitude. Relative to the center of mass, the patterns can then be described as transitions between translation, rotation about a stationary point, or a rotating swarm, where the center of mass undergoes a Hopf bifurcation from steady state to a limit cycle. Examples of some of the stochastic patterns will be given for large numbers of particles.
我们考虑在存在噪声和通信时间延迟的情况下，相互通信或耦合的自驱动粒子系统的随机模式。对于足够大的环境噪声，在具有固定质心的平移状态和旋转状态之间存在转变。时间延迟通信会产生一种依赖于粒子间耦合幅度的分岔模式。在大量极限情况下使用平均场模型，我们展示了在存在通信延迟和耦合幅度时完整的分岔是如何展开的。相对于质心，这些模式随后可描述为平移、绕固定点旋转或旋转群之间的转变，其中质心经历从稳态到极限环的霍普夫分岔。将给出大量粒子的一些随机模式的示例。
