 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/6a/a/solution

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

For

F (n) = α n - β n^{3}

, the nonnegative equilibria are

n = 0, n = K := α / β .

Since

F^{'} (0) = α > 0, F^{'} (K) = α - 3 β K^{2} = - 2 α < 0,

the zero equilibrium is unstable and

K

is asymptotically stable.

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