I'm working on a problem related to predators (R) and pests (P). The formula is as follows:
pn+1= 2.5pn - 0.25rn
rn+1= -1pn + 3.5rn
I have a base case of 10 predators and 10 pests and eigenvalues of 3.707 and 2.292.
I have worked to get: $$ D = \begin{bmatrix}3.707&0\\0.722&-0.872\end{bmatrix} $$
$$ V = \begin{bmatrix}0.770&0.203\\-0.638&-0.979\end{bmatrix} $$
$$ V^-1 = \begin{bmatrix}-1.108&-0.230\\0.722&-0.872\end{bmatrix} $$
How do I now find the number of predators and pests at the end of 7 years, followed by if a population eventually dies out and when?
I hope my current working is correct!
Thanks in advance!