Co-culture Ecosystem

Closed, well-mixed resource→producer→consumer culture (no flow, full remineralization). All quantities in shared nutrient-mass units; total mass is conserved, set by the initial pools.

strip under each slider = stability if only that param varied: stable weakly stable limit cycle unstable Hopf edge no eq.
Producer
Consumer
Type II drives the paradox of enrichment (cycles); Type I gives Lotka–Volterra-like neutral behavior.
Initial conditions
Simulation
Parameters (copy / paste)
Live snapshot of the current state (parameters + initial pools + Type I/II). Edit and Apply to load a set; Copy current also puts it on the clipboard. Off-grid values are kept exactly.
Model equations
dS/dt = recyc − μ(S)P
dP/dt = μ(S)P − g(P)C − m_P·P
dC/dt = ε·g(P)C − m_C·C
μ(S) = μ_max·S/(K_s+S)
g(P) = g_max·P/(K_p+P)
time0
resource0
producer0
consumer0
Scenarios

Population dynamics (time series)

Resource S Producer P Consumer C

Phase portrait — flow field (producer vs consumer)

Streamlines = flow on the conserved 2-D simplex (S = M−P−C). Marker = interior fixed point, colored by its local type: green filled = stable (attractor); blue ring = unstable focus (spirals out, complex λ); red ring = unstable node (no rotation, real λ). Either ring is still encircled by a global limit cycle. Scroll to zoom (toward the cursor); drag to pan when zoomed; double-click to reset.

Live stability

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