psheet4 - • See what happens when you try some harvesting...

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Data Analysis Modelling and Simulation MATH1711 Epiphany Term Practical Sheet 4 Aim : To bring together material from the last two weeks: 1. Experimentation — creating sequences; 2. Solving linear constant coefficient sequence via rsolve and the z -transform ztrans . We are interested in finding out information about nonlinear iterations of the form p n +1 = f ( p n ). We analyse in detail with f ( p ) = ap (1 - p ) 1 but it should be easy to modify this work for any of the nonlinear iterations on the problem sheet. To begin, visit the AiM server. If you complete this weeks task early, then you should consider:
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Unformatted text preview: • See what happens when you try some harvesting in the model, i.e. everything as before except p n +1 = ap n (1-p n )-H where H < a/ 4 and p sufficiently close to 1 / 2 (why to both of these questions?). 2 • Go to the problem sheet and try Qu. 25. • Visit: – Jim Swifts Chaos Web Sites page; – Barry Adams’ Java Bifurcation diagram – Google and do your own search. 1 Note that this is equivalent to Malthus’ model (see Qu. 23). 2 This was Question 6 on the 2002 June exam paper....
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