# Chaotic Hyperjerk Systems

Konstantinos E. Chlouverakis

Department of Informatics and
Telecommunications, University of Athens, Athens 15784, Greece

J. C. Sprott

*Departments of Physics, University
of Wisconsin, 1150 University Avenue, Madison, WI 53706, USA*

Accepted 18 August 2005

### ABSTRACT

A hyperjerk system is a dynamical system governed by an *n*th
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.
Ref: K. E. Chlouverakis and J. C. Sprott,
Chaos Solitons & Fractals 28,
739-746 (2005)

The complete paper is available
in PDF format.

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