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Peer Review

A System of Discrete Dynamical Systems

by Garrett Durand Heath


Overall Rating:

4 stars
Content Quality: 4 stars
Effectiveness: 4 stars
Ease of Use: 5 stars
Reviewed: Apr 18, 2005 by Mathematics
Overview: This site consists of applets that present the graphical and numerical solutions
for first-order, linear, homogeneous and non-homogeneous systems of discrete
dynamical systems. This site is connected to a parent site, Math Tech, that has
been reviewed separately in MERLOT.
Learning Goals: To help students understand the nature of discrete dynamical systems and their
behavior and stability with regard to different values for the parameters and
initial conditions by allowing easy visual experimentation.
Target Student Population: Students taking a course in dynamical systems.
Prerequisite Knowledge or Skills: Some basic knowledge of discrete dynamical systems.
Type of Material: Lecture/presentation with interactive Java applet or targeted supplementary
material for student exploration and practice.
Recommended Uses: Classroom demonstration or self-guided student exercise
Technical Requirements: Java-enabled browser

Evaluation and Observation

Content Quality

Rating: 4 stars
Strengths: The applets are simple and effective and graph the sequences of values resulting
from the userÂ’s choice of parameters and initial conditions. The graph is
color-coded for each sequence in the system and a table of numerical solutions
is also provided for values of n<=50 in the homogeneous system and n<=10,000 in
the non-homogeneous system. A brief analysis of the system is provided and
includes the eigenvalues and eigenvectors, spectral radius, stability and
long-term behavior. The analysis changes to match the parameters selected.
Concerns: In the Points of Interest, reference is made to coupled systems, eigenvectors,
and singular matrices but no mention of these is made in the content of the

Potential Effectiveness as a Teaching Tool

Rating: 4 stars
Strengths: The applets are very nicely presented The user can choose to graph either or
both of the color-coded sequences in the system. The system analysis is simple
and effective. There are a limited number of exercises designed to lead
students to a greater understanding of the behavior of a system of discrete
dynamical systems.
Concerns: There was not any instructional material provided on the how to find
eigenvalues, eigenvectors, spectral radius or how to analyze the long term
behavior. No examples, solutions or explanations were provided with the

Ease of Use for Both Students and Faculty

Rating: 5 stars
Strengths: This site is very simple and easy to use and provides visual examples in an area
not normally included in simpler graphing calculator type applications.
Concerns: Instructor should be prepared to provide additional explanations of the

(Applet failed to run on old Netscape for MAC)

Other Issues and Comments: