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 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.

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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