  Vertically vibrating a liquid bath can give rise to a self-propelled
wave-particle entity on its free surface. The horizontal walking dynamics of
this wave-particle entity can be described adequately by an
integro-differential trajectory equation. By transforming this
integro-differential equation of motion for a one-dimensional wave-particle
entity into a system of ordinary differential equations (ODEs), we show the
emergence of Lorenz-like dynamical systems for various spatial wave forms of
the entity. Specifically, we present and give examples of Lorenz-like 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 wave-particle entity in terms of
Lorenz-like 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 Lorenz-like dynamical systems in
terms of the walking dynamics of a wave-particle entity.
