MAT 1300 Lecture 3: MAT1330 discrete-time dynamical systems intro
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MAT 1300 Full Course Notes
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The number of people who catch the u on campus is equal to half those who had it last year plus 100. xt. This is called a discrete dynamical system. (dynamical because it changes, discrete because it only does so in xed chunks) In general, we can write xt+1 = f (xt) where f is the updating function. 2xt + 100) x0 = 0 x1 = 100 x2 = 150 x3 = 175 x4 = 187. 5 x5 = 193. 75 x6 = 196. 875 x7 = 198. 4375 x8 = 199. 21875 x9 = 199. 609375. We suspect that eventually 200 people will be infected. Homework: what happens if 400 people were initially infected? xt+1 = 1. We could think of this data as the initial and nal size of the endemic period. Therefore plotting xt vs t is complicated, but plotting xt vs xt+1 is easy. We can make a u vaccine, but we need two years usually to know how much to make.
