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Unformatted text preview: in the above equation and plot the graph of the sequence x n and y n against n (good values are n = 200 and a = 0 . 5 ,-. 5). Do you nd comparable behaviour for other values for a ? Malthus population model, a particular choice of pa-rameters Changing an apparently harmless parameter can have a dramatic eect on the behaviour of a nonlinear recurrence relation. Investi-gate the nonlinear recurrence relation y n +1 = ay n (1-y n ) where y (0 , 1) . Notice that if 0 &lt; a &lt; 4 then y n (0 , 1). There are three cases to consider (what is dierent about each?) (a) 0 &lt; a &lt; 1 (try a = 0 . 5); (b) 1 &lt; a &lt; 3 (try a = 1 . 5 , 2 . 5); (c) 3 &lt; a &lt; 4 (try a = 3 . 2 , 3 . 52 , 3 . 58 , 3 . 83.) Try taking lots of dierent starting values y (0 , 1). In the last case, (c), on certain occasions you may want to plot a histogram. To do this type with(stats): with(stats[statplots]): histogram([y(n) $n=0. .100],area=count,numbars=50) ;...
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- Spring '11