 Solution

ID: past-exam-of-the-short-options-course-of-the-university-of-oxford/2023/9/a/iii/solution

The nonnegative quadrant is invariant because both right-hand sides have the corresponding population as a factor. There

u_{2}^{'} \leq ρ γ u_{2}

0 \leq u_{2} (τ) \leq u_{2} (0) e^{ρ γ τ} ⟶ 0 (γ < 0) .

Biologically

γ < 0

δ > r_{2}

: per-capita removal exceeds even the grey squirrels' maximum uncrowded growth rate. Competition can only strengthen the decline.

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