ECEN 4423  Chaotic Dynamics
Catalog Data 
ECEN 4423 (3). Chaotic Dynamics.
Explores chaotic dynamics theoretically through computer simulation.
Covers the standard computational and analytical tools used in
nonlinear dynamics and concludes with an overview of leadingedge chaos
research. Topics include time and phasespace dynamics, surfaces of
section, bifurcation diagrams, fractal dimension, and Lyapunov
exponents.
(Meets with CSCI 4446 and ECEN 5423.)

Credits and Design 
3 credit hours. Elective course.

Prerequisite(s) 
CSCI
1200,
Introduction to Programming,
CSCI
1300,
Computer Science 1: Programming, or
ECEN 1030, C Programming for ECE
PHYS 1110, Physics 1

Recommended prerequisite(s) 
PHYS 1120, Physics 2
CSCI
3656,
Numerical Computation
MATH 3130, Introduction to Linear Algebra.

Textbook 

 
Course Objectives 

Topics Covered 
 General introduction to chaos
 Dynamics of iterated maps
 discrete versus continuoustime chaos: definitions and examples
 return maps: the logistic map
 correlation plot vs. time domain
 stability, attractors, bifurcations
 accumulation points, reverse bifurcations
 Feigenbaum
 Lyapunov exponent and metric entropy
 symbolic dynamics
 stretching, folding, and sensitive dependence
 Sarkovskii and Yorke
 Fractals and fractal dimension
 definitions and examples
 boxcounting dimension
 embedding
 the link between fractals and chaos
 Continuoustime dynamics
 ODE and linear algebra review
 atractors and idssipation: Liouville and Hamilton
 numerical integration
 numerical error
 integratorinduced dynamics: numerical bifurcations and chaos
 Applications
 Lorenz
 Rossler
 driven pendulum
 Poncare sections
 hyperplanes
 visulaization and examples
 algorithms
 Attractor characterization
 definitions
 the variational equation
 location and basin algorithms
 embedding: definitions and algorithms
 numeric Lyapunov algorithms
 experimental Lyapunov algorithms
 attractor dimension algorithms
 fractal basin boundaries
 Hamiltonian chaos
 introduction to classical mechanics
 chaos and KAM torii
 applications: Wisdom, Yip
 Prediction, modeling, and noise
 introduction
 algorithms
 applications
 noise
 Stability
 definitions
 eigenvectors and un/stable manifolds
 homoclinic/heteroclinic orbits
 algorithms
 Farmer's noisereduction scheme
 SmaleBirkhoff: horseshoes and manifolds
 controlling chaos
 Modern topics

Last revised: 080211, PM, ARP.