Chaotic hyperjerk systems

A hyperjerk system is a dynamical system governed by an nth order ordinary differential equation with n > 3 describing the time evolution of a single scalar variable. Such systems are surprisingly general and are prototypical examples of complex dynamical systems in a high-dimensional phase space. This paper describes a numerical study of a simple subclass of such systems and shows that they provide a means to extend the extensive study of chaotic systems with n = 3. We present some simple chaotic hyperjerks of 4th and 5th order. Two cases are examined that are apparently the simplest possible chaotic flows for n = 4, together with several hyperchaotic cases for n = 4 and 5.