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By Mike Mesterton-Gibbons

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Extra resources for A Concrete Approach to Mathematical Modelling (Wiley-Interscience Paperback Series)

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For a = 3, a = 5/2, b = 2, b = 1, x(0) = 1, and j>(0) = 1, the solution is plotted in Fig. 2. Th e IMS L computer package D V E R K produced these graphs, and it might be a useful exercise for you t o duplicate them (your computer center wil l have th e package, or a similar one, and wil l be able to show you how to use it) . { x x 2 2 2 { 2 2 { 2 K 10 Chapte r 1 Growt h and Decay . v. Fig. 20) when a, = 3, a = 5/2, A, = 2, and b = 1. The solid curve is x(t); the dashed curve, y(t). 4 unit s of time.

17) still apply, of course, but the model wil l have t o be altered. Thi s time, each species would grow exponentially in th e absence of the other; whereas, put together, each species would have a restrainin g effect on th e food supply of the other. We would expect thi s effect t o manifest itself as a decrease in growth rate. Let’ s assume that th e decrease for one population is proportiona l t o the size of the other population. 21) μ = α -^χ, 2 2 where a , a are pur e growth rates and by, b are interaction (crowding) parameters.

There are 36, not 37, data points because the uppermost point represents both 1901 and 1902. 29) might even be a better description of overall economic growt h than th e diagram itself, because even the briefest of glances at Fig. , 1917); and such abnormalities may be associated wit h the outlyin g points. 29) as a model of economic growth in Massachusetts. A possible criticis m of thi s proposal immediately springs t o mind. Sup› pose we accept that there is some lin e that captures the essential features of the distributio n of point s in Fig.

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