Projects in Difference Equations
Spring 2000
Coordinator: Dr. M. Kulenovic
Implementation:  Dr. M. Kulenovic and Kenneth P. Wilkinson

     Most people are at least vaguely familiar with the term "chaos", perhaps largely due to the movie Jurassic Park.  The movie is by no means a mathematical discussion but one of the key figures is a mathematician.  With the exception of the dinosaurs, one of the most memorable scenes was Ian Malcolm's enthusiasm in discussing the "butterfly effect".  Paraphrasing Professor Malcolm, a butterfly flapping its wings in Beijing could have a profound influence on the (future) weather in Central Park.
     Crudely stated, chaos is the unpredicatable final result given some small change in initial conditions.  However, chaos can be placed on a firm mathematical footing.  Chaos is a part of the larger field of study known as difference equations.
      Try this simple experiment:  consider some function and apply a random initial value.  Take your output and re-apply it as a new input to the function.  Generate a sequence by using this iterative process.   Now generate a new sequence using the same function with a slightly different initial input.  It would seems reasonable to expect sequences starting off similiar (with the same function) would stay similiar.
      The actual results can be surprising and counter-intuitive.  We may have sequences that start close and stay close or we may have one sequence that is totally unpredictable.  We may find a sequence that is stable or periodic.  The undergraduate Difference Equations course, Mth 442, at the University of Rhode Island, explores these and other exciting ideas.
     This site was created by Dr. M. Kulenovic and the students enrolled in Mth 442 during the Spring Semester of 2000.  As part of the course requirements, students prepared a webpage dealing with different aspects of difference equations.  This site will expand as future Mth 442 students add their projects to these pages.
    Our site was created to give a computer presentation which anyone with some mathematical background could find beneficial.   Listed below are the names of students contributing projects and a link to their page:
Gregg Arpin  Henon's Difference Equation
Cathy Ann Clark Solitons
Peter Dobratz Java Applets
Chad Griep  Riccati Difference Equation
Krzysztof Mailloux Rational Difference Equation
Nicole O'Connell  Lyness' Type Difference Equations
Uriah Petit Mira's Difference Equations
Desire Preira Logistic Difference Equation
Stephanie Seran Lotka-Volterra Difference Equations
Victor Taveras Arnold's Cat Difference Equation

Click here to go to Home Page for Difference Equations at URI