PROGRAM SUMMARY
Title of program:
Ndynamics
Catalogue identifier:
ADKH
Ref. in CPC:
119(1999)256
Distribution format: uuencoded compressed tar file
Operating system: Linux (RedHat 5.2, Debian 2.0.34),Windows 95,98
High speed store required:
32MK words
Number of lines in distributed program, including test data, etc:
74683
Programming language used: Maple, C
Computer: Pentium II 450 PC
Nature of physical problem:
Computation and plotting of numerical solutions of dynamical systems and
the determination of the fractal dimension of the boundaries.
Method of solution
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.
Restrictions on the complexity of the problem
Besides the inherent restrictions of numerical integration methods, this
first version of the package only deals with systems of first order
differential equations.
Typical 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.
Unusual features of the program
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.