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)
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.