Denote the bird and cat population at time k by xk = Ok Rk where k is the time in months, Ok the number of birds in the region studied, and Rk the number of cats (measured in thousands). Suppose: Ok+1 = .5Ok + .4Rk Rk+1 = pOk + 1.1Rk (1) where p is a positive parameter to be specified. The .5 coefficient says that with no cats for food only half of the birds would survive each month, while the 1.1 coefficient says that with no predators, the cats population would grow by 10% each month.

(a) Determine the evolution of this system when the predation parameter p is .104. Since this is about matrices, express the system (1) in a matrix form.

(b) Show that for k sufficiently large xk+1 ' xk and xk ' c () k v where c, are scalars and v a vector to be determined.