Predator-prey dynamical system example
Channel: David Roberts
Date: 2014-06-17

This video analyses the dynamical system given in example 2 on page 94 of the Maths 1A algebra notes, reproduced below.

==== Problem description ====
Consider a simplified predator-prey system in which wood rats are the main diet for owls. At time k, measured in months, x_k = [O_k R_k]^t measures the number O_k of owls and R_k the number of rats in thousands.
Suppose the relationship between the owls and rats is given by

O_{k+1} = (0.5)O_k + (0.4)R_k
R_{k+1} = (-0.104)O_k + (1.1)R_k

[The diagonal entries can be interpreted as: 0.5 indicates if there were no rats, the owl population would halve each month; while 1.1 says the rat population would increase by 10% without owls as predators.]