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}

. The differential inequality, or the Gronwall inequality, gives

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.

 Ancestors (13)

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