Dynamica
A computer package for the study of Discrete Dynamical Systems
and Difference Equations
M. R. S. Kulenovic and Orlando Merino
Department of Mathematics
University of Rhode Island
Kingston, RI 02881
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Dynamica
Dynamica is a computer package,
written in Mathematica, intended for use in the study of difference equations
and discrete dynamical systems.
Let k be a positive integer and let f:Rk
-> R be a given function. A relation of the form
xn+1 = f(xn,
xn-1 , ..,xn-k+1)
is called a difference equation of order k.
Difference equations arise in virtually all areas of science, mathematics
and engineering. Difference equations are discrete analogs of differential
equations.
Dynamica implements a series of
tools and techniques of algebraic, numerical, and graphical nature used
in the study of difference equations. These include:
-
Finding equilibrium and periodic
points.
-
Classifying the stability character
of equilibrium and periodic points.
-
Semicycle analysis of solutions.
-
Calculation and visualization
of invariants (first integrals).
-
Calculation and visualization
of Lyapunov functions.
-
Plotting bifurcation diagrams.
-
Visualization of stable and
unstable manifolds.
-
Calculation and visualization
of Lyapunov numbers.
-
Calculation of Box Dimension.
Dynamica is easy to learn and use.
In very little time the new user may be ready to study complex difference
equations of which not much (maybe almost nothing!) is known. To find out
more about Difference Equations at the University of Rhode Island, visit
www.math.uri.edu/~kulenm/diffeqaturi/dehomepage.html
.
Dynamica is provided with a supplementary
set of Mathematica notebooks, which serve as an illustration of the use
of Dynamica's commands. Take a look at the html versions of the notebooks:
You may download the Dynamica package and
notebooks here.
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The main reference and manual for Dynamica
is the book Discrete Dynamical Systems and Difference Equations with Mathematica,
by M.R.S. Kulenovic and O. Merino, Chapman&Hall/CRC Press, 2002,
For a short description of the book,
go to www.crcpress.com
For a list of corrections to the first edition of the book click
here
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