chaos and modeling

We didn’t (and won’t) go into a whole lot more detail about chaotic dynamics (or the chaotic behaviour of the logistic map) in this class, but here are some ideas and starting points for those who are interested.

• references from the UNDD notes: May (1976), May and Oster (1976)
• the Wikipedia page on the logistic map is not bad
• Devaney (2008) and Strogatz (2014) are good textbooks (I haven’t actually read the second, but anything by Strogatz is worth reading)
• an early review of chaotic dynamics in ecology: Hastings et al. (1993)
• don’t know when it will next be offered, but math 3dc3 covers these models at a deeper mathematical level

As always, further suggestions are welcome.

References

Devaney, Robert. 2008. An Introduction to Chaotic Dynamical Systems. Studies in Nonlinearity. https://www.amazon.com/Introduction-Chaotic-Dynamical-Systems-Nonlinearity-ebook/dp/B00B4LY89S/ref=sr_1_2?ie=UTF8&qid=1505834883&sr=8-2&keywords=devaney+chaos.

Hastings, Alan, Carole L. Hom, Stephen Ellner, Peter Turchin, and H. Charles J. Godfray. 1993. “Chaos in Ecology: Is Mother Nature a Strange Attractor?” Annual Review of Ecology and Systematics 24 (January): 1–33. http://www.jstor.org/stable/2097171.

May, Robert M. 1976. “Simple Mathematical Models with Very Complicated Dynamics.” Nature 261 (5560): 459–67. doi:10.1038/261459a0.

May, Robert M., and George F. Oster. 1976. “Bifurcations and Dynamic Complexity in Simple Ecological Models.” The American Naturalist 110 (974): 573–99. http://www.journals.uchicago.edu/doi/abs/10.1086/283092.

Strogatz, Steven H. 2014. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. 2 edition. Boulder, CO: Westview Press.