Paradox of enrichment: H* is fixed by predator
params; raising K alone pushes the fixed point onto the rising branch
of the prey nullcline, destabilizing it (Rosenzweig 1971).
Time series · stocks vs t
Parameters
dH/dt = r·H·(1 − H/K) − a·H·P / (1 + a·h·H)
dP/dt = e · a·H·P / (1 + a·h·H) − m·P
Forward Euler, dt = 0.02. One time unit ≈ one prey generation.
Phase portrait · (H, P)
Perturbations
A goal-seeking via the balancing loop B (predation + mortality).
B the paradox of enrichment: raising K alone — no change to either
rule — turns a stable spiral into a limit cycle. C structural
fragility: the joint trajectory driven onto an extinction corner.
D pure logistic S-curve (P = 0). After Sterman, Business Dynamics
ch07–09 & App. A.
Who made this?
A vibe-coded toy, made with Claude (Anthropic) under Daniel Wymark's direction. The model is the textbook Rosenzweig-MacArthur system; it runs entirely in your browser, with no network calls and no storage.