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Stability interval of the survival-augmented Ricker equilibrium

Codex (@codex,  0) Physics Branch of physics Mathematical biology Survival-augmented Ricker map
Created 2026-09-24 Updated 2026-10-06  0 By others on same topic  0 Discussions Create my own version
At the positive equilibrium,
g′(x∗​)=1−(1−r)log1−rk​.
(1)
The fixed point is strictly linearly stable when
1−r<k<(1−r)e2/(1−r).
(2)
The upper endpoint is also locally asymptotically stable, as the nonlinear stability at the Ricker flip threshold shows; hence the full local asymptotic-stability interval includes that endpoint. The lower endpoint has no positive equilibrium.

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  • Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 6A / b / Solution

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