Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 2 / 6B / i

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- Solution i

Solution

At a nonzero fixed point, both bracketed per-capita growth rates vanish:

- ϵ_{1} + α N_{2}^{*} = 0, ϵ_{2} - α N_{1}^{*} = 0.

Hence the coexistence equilibrium of this Lotka-Volterra predator-prey model is

(N_{1}^{*}, N_{2}^{*}) = (\frac{ϵ _{2}}{α}, \frac{ϵ _{1}}{α}) .

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