•The model

From data it is possible to derive a model that describes the size of the owl and squirrel populations in a given month as functions of the population sizes the preceding month--a discrete dynamical system.  (To lean how to fit such a model to the data, see [links to be supplied].)  The model you will use is as follows.

At a given time t, measured in months, denote by o(t) the number of spotted owls and by s(t) the number of thousands of flying squirrels.  Then in the following month there will be, according to this model, 0.4 o(t) + 0.3 s(t) spotted owls and -0.5 o(t) + 1.2 s(t) thousands of flying squirrels.  In other words:

 

    o(t + 1) =      0.4 o(t) + 0.3 s(t), s(t + 1) = -0.5 o(t) + 1.2 s(t)

The model used here appears in Exercise 5, Section 5.6, of David C. Lay, Linear Algebra and Its Applications, 2nd ed.Addison-Wesley, Reading, Mass., 2000, page 346.

 Converted by Mathematica  (September 5, 2002)