|
Overview of 660 Topics
|
|
Topic
|
Reading
|
Introduction
to Dynamical Systems
|
Chapter 1
|
1-D
flows, Fixed Points and Stability
|
Chapter 2
|
Scaling,
Dimensional Analysis
|
Sec 2.4,
2.6, Handout
|
Saddle-Node,
Transcritical and Pitchfork Bifurcations
|
Sec 3.1,
3.2, 3.4
|
Imperfect
Bifurcation & Catastrophes
|
Sec 3.6
|
Linear
Systems in 2-D
|
Sec 5.1,
5.2
|
Phase
Portraits, Fixed points, and Linearization
|
Sec 6.1,
6.3
|
Mechanical,
Conservative and Reversible Systems
|
Sec 6.5,
6.6, 6.7
|
Van der
Pol Oscillator
|
Sec 7.1
|
Closed
Orbits – No Way!
|
Sec 7.2
|
Poincaré-Bendixson
Theorem
|
Sec 7.3
|
Liénard
Systems
|
Sec 7.4
|
Relaxation
Oscillations
|
Sec 7.5
|
Weakly
Nonlinear Oscillators
|
Sec 7.6
|
Perturbation
Theory, Poincaré-Lindstedt Method,
Averaging, Method of Multiple Scales
|
Handout
|
Duffing
Equation, Forcing and Resonance
|
Handout
|
Bifurcations
in Higher Dimensional Systems
|
Sec 8.1
|
Hopf
Bifurcations
|
Sec 8.2,
8.3, Kuz 2.3, 3.4, 3.5
|
Center
Manifold Theory
|
Kuz 5.2,
5.3, Handout
|
Lorenz
Equations
|
Sec 9.1,
9.2, 9.3
|
Lorenz
Map, Poincaré Map
|
Sec 9.4
|
Cobwebs
|
Sec 10.1
|
Logistic
Map
|
Sec
10.2, 10.3
|
Periodic
Windows
|
Sec 10.4
|
Lyapunov
Exponent
|
Sec 10.5
|
Renormalization
|
Sec
10.7, Handout
|
2-D Maps
|
Handout
|
Fractals
and the Cantor Set
|
Sec
11.0, 11.1, 11.2, Handout
|
Chaos
and Strange Attractors
|
Sec
12.3, Handout
|
|
|
