Section: SAMID1MU: Modeling using dynamical systems | IEAP Master's prerequisites: to do before the first classes

Section outline

Before the first class, which will take place on Sept. 3, you are asked to read the two book chapters included below, on discrete-time dynamical systems (essentially, iterating maps).
Like in other courses, you will use Python notebook. One notebook is attached below, please go through it and play with the code included, which corresponds to exercise 1.1 from the chapter by Kaplan & Glass. You should also try out with another map, which is proposed below that exercise in the notebook.
Overall, we will rapidly need to manipulate derivatives (when working with continuous-time dynamical systems. So make sure you understand this part of the mathematical prerequisites proposed in the document by E. Le Clezio.
See you on Sept. 3!
- Select activity Notebook: Discrete dynamical systems
  
  Notebook: Discrete dynamical systems File
  
  Jupyter notebook to run and play with, in particular changing parameter values (R in the first example) as well as initial conditions. Then you can observe the behaviour of iterates for N large enough.
  TODO: add comments to explain what each part of the code does.
- Select activity Chapter 1 from "Understanding nonlinear dynamics" by L. Kaplan & L. Glass
  
  Chapter 1 from "Understanding nonlinear dynamics" by L. Kaplan & L. Glass File
  
  Please read until section 1.4 included (p. 11 of the chapter, p. 30 of the PDF) and make exercise 1.1 using the provided notebook.
- Select activity Chapter 10 from "Nonlinear dynamics and chaos" by S. Strogatz
  
  Chapter 10 from "Nonlinear dynamics and chaos" by S. Strogatz File
  
  This is complementary to the other chapter. Read until p. 362 included (p. 8 of the PDF).