12.006J | Fall 2022 | Undergraduate

Nonlinear Dynamics: Chaos

Calendar

SES # LECTURE TOPICS DUE DATES
1 Introduction to Nonlinear Dynamics: Chaos  
2 Flows and Bifurcations in One Dimension  
3 Flows and Bifurcations in One Dimension (cont.) Problem Set 1 due
4 Pendulum and Stability in Two Dimensional Systems  
5 Pendulum and Stability in Two Dimensional Systems (cont.)  Problem Set 2 due
6 Dissipation and Contraction of Volumes in Phase Space  
7 Dissipation and Contraction of Volumes in Phase Space (cont.)  
8 Forced Oscillators and Limit Cycles  
9 Forced Oscillators and Limit Cycles (cont.)  
10 Bifurcations in Two Dimensions  
11 Bifurcations in Two Dimensions (cont.) Problem Set 3 due
12 Spectral Analysis for Dynamical Systems  
13 Spectral Analysis for Dynamical Systems (cont.) Problem Set 4 due
14 Spectral Analysis for Dynamical Systems (cont.)  
15 Poincaré Sections  
16 Poincaré Sections (cont.) Problem Set 5 due
17 Fluid Dynamics and Rayleigh-Benard Convection  
18 Fluid Dynamics and Rayleigh-Benard Convection (cont.) Problem Set 6 due
19 Introduction to Strange Attractors Problem Set 7 due
20 Lorenz Equations Final Project Topic and Brief Summary due
21 Lorenz Equations (cont.)  
22 Hénon Attractor Problem Set 8 due
23 Fractal Dimension  
24 Lyapunov Exponents Problem Set 9 due
25 Period Doubling Route to Chaos  
26 Period Doubling Route to Chaos (cont.)  
27 Period Doubling Route to Chaos (cont.) Problem Set 10 due
28 Intermittency (and Quasiperiodicity)  
  Final Project Oral Presentation Final Project Written Report due

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