Mier-Y-Teran-Romero Luis, Lindley Brandon, Schwartz Ira B
U.S. Naval Research Laboratory, Code 6792, Nonlinear System Dynamics Section, Plasma Physics Division, Washington, DC 20375, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056202. doi: 10.1103/PhysRevE.86.056202. Epub 2012 Nov 5.
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments.
我们研究离散、随机分布的时间延迟对自推进粒子耦合系统动力学的影响。对该系统的平均场近似进行分岔分析表明，该系统具有某些具有普遍特征的模式，这些模式取决于时间延迟分布的特征矩。具体而言，我们通过理论和数值方法表明，尽管简单模式（如平移）的分岔仅作为时间延迟分布一阶矩的函数而改变稳定性，但由霍普夫分岔产生的更复杂模式则取决于所有矩。
