| We ek |
Date | Contents | |
| 1 | 0102 |
UBC closed | |
| 0104 | Outline Overview; examples of the geometric approach |
L01 |
|
| 0106 | PART I. One dimensional
flows §2.1-2.3 one dimensional flow, fixed points, their stability by graph |
L02 | |
| 2 | 0109 | §2.4 stability analysis by linear approximation,
exceptional cases §2.5 unique existence theorem (statement) |
L03 |
| 0111 |
examples of
nonuniqueness and blow-up. No
crossing. §2.6 no oscillation in 1D flows. §2.7 potential |
L04 | |
| 0113 |
potential continued; (we skip §2.8) §3.1 saddle-node bifurcation, bifurcation diagram |
L05 | |
| 3 | 0116 |
normal form §3.2 transcritical bifurcation |
L06 |
| 0118 |
normal form and 2nd example of transcritical bifurcation
§3.4 pitchfork bifurcation |
L07 | |
| 0120 |
supercritical and
subcritical pitchfork bifurcation, normal
form |
L08 | |
| 4 | 0123 | subcritical pitchfork
with higher order
damping §3.5 example: damped bead on a rotating hood |
L09 |
| 0125 | §3.6 imperfect bifurcations (bifurcations with 2
parameters) |
L10 | |
| 0127 |
§3.7 example: insect outbreak fixed point surface in k-r-x space: graph and Maple code (you can rotate it in Maple) |
L11 | |
| 5 | 0130 |
PART II. Two
dimensional
flows §5.1-5.2 2D linear flows |
L12 |
| 0201 |
§6.1-6.3
fixed points and linearizations |
L13 | |
| 0203 |
§6.3-6.4 examples, competition models |
L14 | |
| 6 | 0206 |
§6.5 conservative systems |
L15 |
| 0208 |
(continue) §6.6 reversible systems |
L16 | |
| 0210 |
examples |
L17 | |
| 7 | 0213 |
§6.7 example: pendulum |
L18 |
| 0215 |
basin of attraction for damped pendulum §6.8 index theory |
L19 |
|
| 0217 |
Midterm exam |
||
| 0220-0224 | Midterm break | |
|
| 8 | 0227 |
index theory continued Chapter 7 limit cycles |
L20 |
| 0229 |
§7.1 examples §7.2 ruling out closed orbits: gradient flows |
L21 | |
| 0302 |
Liapunov functions and
Dulac's criterion §7.3 Poincare-Bendixson theorem: statement |
L22 | |
| 9 | 0305 |
applications of the
Poincare-Bendixson theorem. figures for example 7.3.2: a, b |
L23 |
| 0307 |
§7.4 Lienard equation |
L24 | |
| 0309 |
Chapter 8 bifurcations for 2D systems §8.1 Effectively one-dimensional bifurcations for 2D systems §8.2 Hopf bifurcation |
L25 | |
| 10 | 0312 |
Hopf bifurcation
continued |
L26 |
| 0314 |
§8.3 example: oscillating chemical reactions links: wikipedia, youtube video 1, youtube video 2 |
L27 | |
| 0316 |
§8.7 Poincare map and its linear
stability |
L28 | |
| 11 | 0319 |
PART III. Chaos
and strange attractors §8.6 quasi-periodic flows: a trajectory that is dense on a torus §9.2 Lorenz equations. youtube videos: Lorenz waterwheel, Lorenz attractor. |
L29 |
| 0321 |
Lorenz equations continued |
L30 | |
| 0323 |
§9.3 chaos on a strange attractor |
L31 | |
| 12 | 0326 |
§9.5 global behavior for different parameter
values §10.1 one dimensional maps, fixed points and cobwebs |
L32 |
| 0328 |
§10.2-10.3 logistic map |
L33 | |
| 0330 |
§10.4 periodic windows §10.6 universality |
L34a L34b | |
| 13 |
0402 |
§11.2
Cantor sets §12.1-12.2 examples of stretching and folding for strange attractors |
L35 |
| 0404 |
review |
||
| 0406 |
Good Friday |
||
| 0413 |
Final
Exam 3:30-6pm |
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