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Rosenzweig-MacArthur equilibrium and enrichment stability: Hopf boundary · case 04

The exact Hopf bifurcation point is labelled stable.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Type II predator-prey: N* = m/(a(e-hm)) requires e>hm and N*<K else ['predator-extinct', [K, 0]]; P* = (r/a)(1-N*/K)(1+ahN*); hump = (K-1/(ah))/2 for h>0 else -1; stable if N*>hump, 'hopf' if equal, else 'cycles'; values rounded 6; None for invalid parameters.

Why this case matters

Population projections set harvest quotas, conservation status and pest-control timing; a wrong update order, boundary or rate conversion silently changes management advice.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression: exact hopf point	`["stable", [4.0, 1.8]]`	`["hopf", [4.0, 1.8]]`	Failed

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