1. Stable coexistence under mild competition
Ecology instructorBackground
A lecture needs a concrete case where both species persist at an interior equilibrium.
Problem
Show that when both α’s lie below the K-ratio thresholds, the isoclines cross stably and the trajectory converges to coexistence.
How to use
Enter r₁=0.5, r₂=0.4, K₁=100, K₂=80, α₁₂=0.6, α₂₁=0.5, N₁(0)=10, N₂(0)=8, tMax=60.
r1=0.5, r2=0.4, k1=100, k2=80, alpha12=0.6, alpha21=0.5, n10=10, n20=8, tMax=60Outcome
Both α’s are below their thresholds (K₁/K₂=1.25, K₂/K₁=0.8). The phase plane shows the trajectory settling on the coexistence point (N₁*, N₂*)=(74.29, 42.86).