S17 Class 03: Bifurcations in 1d


Class 03:
Before class, watch the lecture material linked below
Post at least one question or comment on Piazza (access via Canvas or directly).  See "Check Yourself" Q1 for details.
Check yourself via the Class 03 Check Yourself on Canvas (Due by 11:59pm on Sun Jan 29)
In class, we'll work on examples of these ideas: (see file below)
After class, complete the homework (problems due Friday Feb 3rd)

Video summary:
Watch Approximating solutions to diff eqs video (12 min)
Watch L2  by Steve from 32:45 to the end (42 min),
Watch the Subcritical pitchfork video (7 min)
Corresponding text: sections 2.8, 3.0-3.4

Total: 61 minutes of lecture


Note: For videos, by clicking on the gear symbol you can change the speed of the video replay (and can turn on closed captions).

Video clips from above broken down by topic:
V00 (Sarah) | Approximating solutions to diff eqs  |  12 min
V01 (St)  |  Bifurcations  (32:45 to 39:00)  |  6 min
V02 (St)  |  Saddle node  (39:35 to 45:16)  |  5 min
V03 (St)  |  Bifurcation diagram  (45:16 to 50:00)  |  5 min
V04 (St)  |  Example  (50:10 to 1:03:15)  |  13 min
V05 (St)  |  Transcritical  |  (1:03:15 to 1:11:15)  |  8 min
V06 (St)  |  Pitchfork  |  (1:11:15 to 1:16)  |  5 min
V07 (Sarah)  |  Subcritical pitchfork  (All)  |  7 min

Related objectives:
-  identify and describe the importance of bifurcations, by which we mean qualitative changes in system behavior that occur as a parameter is varied
- classify bifurcations and identify symmetries or constraints that correspond to particular bifurcations

activity17-01-30_bifurcations.pdf175 KB