Nonlinear dynamical models and jerky motion

We investigate the connection between one-dimensional Newtonian jerky dynamics and nonlinear dynamical systems in a three-dimensional phase space. With exact transformations, we show that the Rössler model, as well as the Lorenz model, can be interpreted as jerky motion and discuss whether they are Newtonian or not. Moreover, Sprott’s model R is identified as one of the simplest Newtonian jerky dynamics that can lead to chaos. Using a wide class of jerk functions, we derive a criterion for being Newtonian jerky.