Sustainability Triangle: Economy–Environment–Society Dynamics

Feedback Strengths

Resource extraction rate 1.00×

Environmental regeneration 1.00×

Equity investment 1.00×

Live Stocks

Economy

50%

Environment

60%

Society

40%

Weakest-link sustainability index 40%

Simulated time

0.0 yr

Trajectory state

Running

How it works

The three-pillar model of sustainability treats an economy, its environment and its society as three coupled stocks K, N, S ∈ [0,1] evolving under a nonlinear feedback system, integrated here with explicit Euler steps:

dK/dt = rK·K·(1−K) − eX·K·(1−N)
dN/dt = rN·N·(1−N) − eX·gX·K·N
dS/dt = rS·eQ·(K+N)/2·(1−S) − dS·S·(1−K)·(1−N)

K (economy) grows logistically toward its own carrying capacity but is throttled when the environment N is depleted; N regenerates logistically but is drawn down by economic extraction proportional to K·N; S (social equity) rises when investment from a healthy K and N flows in, and erodes when both economy and environment underperform at once. rK, rN, rS are fixed intrinsic rates; eX (extraction), gX (regeneration) and eQ (equity investment) are the three sliders.

Weakest-link index = min(K, N, S) × 100 — the classical "three-pillar" claim that overall sustainability is bounded by its worst-performing pillar, not their average.
Resource shock instantly cuts N by 40%, letting you watch whether the system's feedback loops pull it back toward a stable point or push it into collapse.
The 3D trail is the system's trajectory through (K, N, S) phase space — a stable sustainable regime spirals into a fixed point; an over-extractive regime spirals toward the N≈0 wall.

This is the same coupled-stock structure used in ecological-economics system-dynamics models (e.g. the World3 family): no single sector can be optimized in isolation because each one's growth term depends on the state of the other two.

Stable

Economy (K) — X axis Environment (N) — Y axis Society (S) — Z axis

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