A recent model of Ariel et al. (2017) for explaining the observation of Lévy walks in swarming bacteria suggests that self-propelled, elongated particles in a periodic array of regular vortices perform a super-diffusion that is consistent with Lévy walks. The equations of motion, which are reversible in time but not volume preserving, demonstrate a new route to Lévy walking in chaotic systems. Here, the dynamics of the model is studied both analytically and numerically. It is shown that the apparent super-diffusion is due to “sticking” of trajectories to elliptic islands, regions of quasi-periodic orbits reminiscent of those seen in conservative systems. However, for certain parameter values, these islands coexist with asymptotically stable periodic trajectories, causing dissipative behavior on very long time scales.

Ariel等人的最新模型。（2017）解释了Lévy游走在成群细菌中的观察结果表明，周期性规则涡流中自推进的细长粒子会执行与Lévy游走一致的超扩散。运动方程在时间上是可逆的，但不能保持体积，这表明在混沌系统中通往列维行走的新途径。在此，对模型的动力学进行了分析和数值研究。结果表明，明显的超扩散是由于轨迹“粘”在椭圆形岛上，而椭圆形岛的准周期轨道区域使人联想到保守系统中的轨道。但是，对于某些参数值，这些岛与渐近稳定的周期轨迹共存，从而在很长的时间尺度上导致耗散行为。