Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

[Licence| Download | New Version Template] adkh_v1_0.tar.gz(2554 Kbytes)
Manuscript Title: Numerical analysis of dynamical systems and the fractal dimension of boundaries.
Authors: L.G.S. Duarte, L.A.C.P. da Mota, H.P. de Oliveira, R.O. Ramos, J.E.F. Skea
Program title: Ndynamics
Catalogue identifier: ADKH_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 119(1999)256
Programming language: Maple, C.
Computer: Pentium II 450 PC.
Operating system: Linux (RedHat 5.2/Debian 2.0.34), Windows 95/98.
RAM: 32M words
Keywords: General purpose, Differential equation, Maple, Dynamical systems, Fractal dimension, Symbolic computing.
Classification: 4.3.

Nature of problem:
Computation and plotting of numerical solutions of dynamical systems and the determination of the fractal dimension of the boundaries.

Solution method:
The default method of integration is a 5th order Runge-Kutta scheme, but any method of integration present on the MAPLE system is available via an argument when calling the routine. A box counting method is used to calculate the fractal dimension of the boundaries.

Besides the inherent restrictions of numerical integration methods, this first version of the package only deals with systems of first order differential equations.

Unusual features:
This package provides user-friendly software tools for analyzing the character of a dynamical system, whether it displays chaotic behaviour, etc. Options within the package allow the user to specify characteristics that separate the trajectories into families of curves. In conjunction with the facilities for altering the user's viewpoint, this provides a graphical interface for the speedy and easy identification of regions with interesting dynamics. An unusual characteristic of the package is its interface for performing the numerical integrations in C using a 5th order Runge-Kutta method. This potentially improves the speed of the numerical integration by some orders of magnitude and, in cases where it is necessary to calculate thousands of graphs in regions of difficult integration, this feature is very desirable.

Running time:
This depends strongly on thE dynamical system. WIth a Pentium II 450 PC with 128 Mb of RAM, the integration of one graph (among the thousands it is necessary to calculate to determine the fractal dimension) takes from a fraction of a second to several seconds. The time for plotting the graphs depends on the number of trajectories plotted. If there are a few thousand, this may take 20 to 30 seconds.