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 (2006)
The complete paper is available
in PDF format.
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