 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-2/6c/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

x = \frac{N _{1}}{K _{1}}, y = \frac{N _{2}}{K _{2}}, τ = r_{2} t .

Then

x^{'} = ρ x (1 - x - α y), y^{'} = y (1 - β x) .

(0, 0), (1, 0), (\frac{1}{β}, \frac{1 - β ^{- 1}}{α}),

where the coexistence state is biologically relevant exactly when

β > 1

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