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Feedback Loop Simulator

Iteration, gain, and delay in discrete dynamical maps

Explore how feedback shapes dynamics. The cobweb diagram traces iteration of x_{t+1} = f(x_t): vertical to the curve, horizontal to the identity line. Adjust gain to cross the stability threshold -- watch convergence become divergence. Add delay to see how lagged feedback generates oscillations even in stable systems.

Fixed point: x* = 0 (stable)
0.00.20.40.60.81.0x0.00.20.40.60.81.0f(x)f(x)y = xcobweb

The cobweb diagram traces iteration: from x, go vertical to f(x), then horizontal to y = x. Convergence means negative feedback dominates; divergence means positive feedback wins.

Feedback Loop Simulator -- Systems Thinking Labs · hbar.university