Jun 25, 2024  
2018-2019 Undergraduate Academic Catalog 
2018-2019 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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EE 4060 - Introduction to Nonlinear Dynamics and Chaos

2 lecture hours 2 lab hours 3 credits
Course Description
This course introduces the student to the basic concepts of nonlinear dynamics and chaos via numerical simulations and electric circuits. The primary goal is to understand the bifurcations and steady-state behavior of nonlinear dynamical systems. The secondary goal is to study the phenomenon of chaos using computer simulation and physical circuits. In addition, due to the graduate nature of the course, students will be asked to work on a more challenging project, as opposed to the undergraduate course offering. (prereq: MA 235 , EE 2050  or EE 201 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Describe the fundamental differences between linear and nonlinear dynamical systems and the importance of studying nonlinear dynamics
  • Define the different bifurcation phenomenon of nonlinear systems in one, two and three dimensions
  • Apply bifurcation analysis to study practical systems such as oscillator circuits
  • Understand the concepts of Fractal dimensions, Poincare map and Lyapunov Exponents
  • Understand how to use circuit elements and devices to build nonlinear circuits
  • Perform literature review
  • Understand how to use circuit elements and devices to build nonlinear circuits

Prerequisites by Topic
  • Understanding of linear constant coefficient ODEs
  • Basic circuit analysis

Course Topics
  • Fixed Points and Stability (1 class)
  • Circuit elements and devices (3 classes)
  • Bifurcations in one dimensions (3 classes)
  • Midterm (1 class)
  • Introduction to chaotic systems (1 class)
  • Analyzing chaotic systems - Routes to Chaos (2 classes)
  • The phase plane - linear systems, limit cycles (two dimensional systems)

Laboratory Topics
  • Laboratory experiment details and requirements are described in [1]
  • Students are expected to prepare for the lab by doing all required pre-lab activities

Joshua Carl

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