Math 339, Lecture Notes and Sources
- Lecture #1 (Thursday September 5th)
- Lecture #2 (Tuesday September 10th)
- lecture notes prepared
before the lecture by Rebecca
- lecture notes taken
during the lecture by Hong Anh Tran (thank you very much!)
-
Maple Code for the phase plane analysis of the Opinion
Dynamics model in Baumgaertner et al (2018) (see the link for the
opinion dynamics research paper in lecture #1). Note that
clicking on this link will get you gobbledygook, but if you
right-click and download the file, you will have a .mw file that
Maple can interpret.
-
Maple Output (pdf format) for the phase plane analysis of the Opinion
Dynamics model in Baumgaertner et al (2018) (see the link for the
opinion dynamics research paper in lecture #1)
- pplane
system for the Opinion Dynamics model, for those of you who have
access to Matlab. You will also
need pplane9 . Again, clicking
on these links gives you gobbledygook. Download the files and open
them using matlab.
- Lecture #3 (Thursday September 12th)
- lecture notes prepared
before the lecture by Rebecca
- lecture notes taken
during the lecture by Hong Anh Tran (thank you very much!)
- Lecture #4 (Tuesday September 17th)
- lecture notes prepared
before the lecture by Rebecca
- lecture notes taken
during the lecture by Hong Anh Tran (thank you very much!)
- Lecture #5 (Thursday September 19th)
- lecture notes prepared
before the lecture by Rebecca
- lecture notes taken
during the lecture by Hong Anh Tran (thank you very much!)
- Lecture #6 (Tuesday September 24th)
- lecture notes prepared
before the lecture by Rebecca
- lecture notes taken
during the lecture by Hong Anh Tran (thank you very much!)
- While the opinion dynamics model that we have been studying gives
us a look at the effect of mixing, the dynamics in the absence of
mixing are harder to study, as the ODE is, implicitly, a fully-mixed
system. It turns out that, in order to get polarization,
which is a real problem these days, you need less mixing. We
discuss opinion dynamics with low mixing
in this paper, using an
individual-based model. You might find it interesting! It suggests
that, if the internet is working more as a venue where mixing is
decreased, because search engines (especially youtube) tend to show
you content that you already like, the likelihood of polarization is
increased.
- Lecture #7 (Thursday September 26th)
- lecture notes prepared
before the lecture by Rebecca
- lecture notes taken
during the lecture by Hong Anh Tran (thank you very much!)
- Lecture #8 (Tuesday October 1st)
- Guest lecture given by Dr Eric Foxall
- lecture notes taken
during the lecture by Hong Anh Tran (thank you very much!)
- Lecture #9 (Thursday October 3rd)
- lecture notes prepared
before the lecture by Rebecca
- lecture notes taken
during the lecture by Hong Anh Tran (thank you very much!)
- Lecture #10 (Thursday October 10th)
- Lecture #11 (Tuesday October 15th)
- lecture notes prepared
before the lecture by Rebecca. This lecture and lecture #12 are a
presentation of the modelling work presented in a series of three papers.
Links to the two papers discussed today appear below.
- This lecture was based mostly on
the 1st
plankton-oxygen dynamics paper.
- The two-parameter bifurcation diagram that was presented at the end of
the lecture came from
the 2nd
plankton-oxygen dynamics paper, page 106 (page 16 of 19). Note also
Figure 4 on page 96 (6 of 19): This figure shows the different behaviours
that the system can exhibit, including the oscillations resulting from the
Hopf bifurcation we discussed in class.
- Lecture #12 (Thursday October 17th)
- Lecture #13 (Tuesday October 22nd)
- lecture notes prepared
before the lecture by Rebecca.
- This lecture was based on material from sections 7.4 and 7.5 of the book
"Chaos: An Introduction to Dynamical Systems" by Alligood, Sauer, and Yorke,
available
on Springerlink
(the link should give you free access to the pdf
of the book if you are on campus).
- Lecture #14 (Thursday October 24th)
- lecture notes prepared
before the lecture by Rebecca.
- This lecture was based on material from section 7.6 of the book
"Chaos: An Introduction to Dynamical Systems" by Alligood, Sauer, and Yorke,
available
on Springerlink
(the link should give you free access to the pdf
of the book if you are on campus).
- Lecture #15 (Tuesday October 29th)
- lecture notes prepared
before the lecture by Rebecca.
- This lecture was based on material from section 8.1 of the book
"Chaos: An Introduction to Dynamical Systems" by Alligood, Sauer, and Yorke,
available
on Springerlink
(the link should give you free access to the pdf
of the book if you are on campus).
- Lecture #16 (Thursday October 31st)
- Lecture #17 (Tuesday November 5th)
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