chalkdust

The Telefunken RA 770 analogue computer.

The most prominent feature of such a machine is the patch field, which is on the far right of the picture above. Here all of the inputs and outputs of the literally hundreds of individual computing elements are brought together. Using (shielded) patch cords, these computing elements are connected to each other, seing up the desired model. In the middle are the manual controls (start/stop a computation, set parameter values, etc) and an oscilloscope to display the results as curves. On the upper far le is a digital extension that allows us to set up things like iterative operations, where one part of the computer generates initial conditions for another part. Below le are eight function generators, which can be manually set to generate rather arbitrary functions by a polygonal approximation.

A more complex example Let us now look at a somewhat more complex programming example: the investigation of a predatorprey model as described by Alfred James Lotka in 1925 and then Vito Volterra in 1926. This consists of a closed ecosystem with only two species, foxes and rabbits, and an unlimited food supply for the rabbits. Rabbits are removed from the system by being eaten by the foxes—without this mechanism their population would just grow exponentially. Foxes, on the other hand, need rabbits for food, or they would die of starvation. This system can be modelled by two coupled diﬀerential equations with r and f denoting the number of rabbits and foxes respectively: r˙ = α1 r − α2 rf f˙ = −β1 f + β2 rf

(3) (4)

The change in the rabbit population, r,˙ involves the fertility rate α1 and the amount of rabbits that are killed by foxes, denoted by α2 rf. The change in the fox population, f,˙ looks quite similar but 57

spring 2016

Chalkdust, Issue 03

Popular mathematics magazine from UCL

Chalkdust, Issue 03

Popular mathematics magazine from UCL