Lorenzlike systems emerging from an integrodifferential trajectory equation of a onedimensional waveparticle entity
Abstract
Vertically vibrating a liquid bath can give rise to a selfpropelled waveparticle entity on its free surface. The horizontal walking dynamics of this waveparticle entity can be described adequately by an integrodifferential trajectory equation. By transforming this integrodifferential equation of motion for a onedimensional waveparticle entity into a system of ordinary differential equations (ODEs), we show the emergence of Lorenzlike dynamical systems for various spatial wave forms of the entity. Specifically, we present and give examples of Lorenzlike dynamical systems that emerge when the wave form gradient is (i) a solution of a linear homogeneous constant coefficient ODE, (ii) a polynomial and (iii) a periodic function. Understanding the dynamics of the waveparticle entity in terms of Lorenzlike systems may provide to be useful in rationalizing emergent statistical behavior from underlying chaotic dynamics in hydrodynamic quantum analogs of walking droplets. Moreover, the results presented here provide an alternative physical interpretation of various Lorenzlike dynamical systems in terms of the walking dynamics of a waveparticle entity.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09754
 Bibcode:
 2021arXiv211009754V
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Fluid Dynamics
 EPrint:
 10 pages, 5 figures