Conservative, dissipative and super-diffusive behavior of a particle propelled in a regular flow

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Abstract

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.

Original languageEnglish
Article number132584
JournalPhysica D: Nonlinear Phenomena
Volume411
DOIs
StatePublished - Oct 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

  • Chaos
  • Lévy walk
  • Mixed dynamics
  • Regular island
  • Reversible systems
  • Super-diffusion

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