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Chaos and nonlinearity

This is our first lecture that will emphasize the improtance of nonlinearity.  By nonlienarity we really mean non-linear per capita growth rates, and the potential for complex dynamics.  If population numbers are variable through time, is it noise (external forces) or internal dynamics that is driving the system.  We'll begin by defining the question and giving bakcground, then going through some of the basics of chaos and nonlinear dyanmics.  We'll draw some examples from the epidemiological literature.


* means required reading

Chaos in Ecology: Is Mother Nature a Strange Attractor?  Alan Hastings, Carole L. Hom, Stephen Ellner, Peter Turchin, H. Charles J. Godfray   Annual Review of Ecology and Systematics, Vol. 24. (1993), pp. 1-33.

*  Ellner, SP; Bailey, BA; Bobashev, GV; Gallant, AR; Grenfell, BT; Nychka,  DW.  Noise and nonlinearity in measles epidemics: Combining mechanistic and  statistical approaches to population modeling.  AMERICAN NATURALIST, MAY, 1998, V151(N5):425-440.