On Nonlinear Dynamical Systems Topologically Conjugate to Jerky Motion via a Linear Transformation

In a recent paper, it was shown that members of a class of three-dimensional nonlinear dynamical systems are equivalent to jerky dynamics. The transformations used have the restriction that the state variable in the jerky dynamics is the same as one of the state variables of the three-dimensional system. As a consequence, some of the transformations used are necessarily nonlinear. We show that by removing this restriction, some of these systems can be transformed to jerky dynamics via affine transformations. In particular, we give conditions under which the system is topologically conjugate to jerky dynamics via an affine transformation.