Roy Choudhury, University of Central Florida


Complementary Approaches to Understanding Chaotic Systems

Abstract: n this tutorial talk, we will introduce three complementary modern approaches which reveal different facets of chaotic regimes in a variety of nonlinear systems. The techniques will be illustrated using the famous Lorenz Equations, as well as recent `hyper-chaotic' systems where the information thus obtained will prove invaluable. The methods we discuss are:

a. traditional bifurcation sequences leading from ordered regimes to chaos;

b. a technique based on Shilnikov's Theorems which rigorously confirms the existence of chaos. Without this, numerically observed chaotic behavior, may merely be a numerical artifact, or so-called `numerically-generated chaos';

and

c. the recently-developed technique of `competitive modes' which helps delineate parameter regimes where chaos is likely to occur. This is of general interest, but particularly important in systems with a large number of parameters, such as biological and optical models, where chaotic regimes might otherwise be virtually impossible to identify in the high-dimensional parameter space.


Address: Department of Mathematics, University of Central Florida, 4000 Central Florida Blvd. P.O. Box 161364, Orlando, FL 32816-1364. Go to Professor Choudhury's website.