A recent model of Ariel et al. [1] for explaining the observation of Levy 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 Levy walks. The equations of motion, which are reversible in time but not volume preserving, demonstrate a new route to Levy 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.
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