Tool

OGY chaos control

OGY (Ott-Grebogi-Yorke, 1990) stabilises one of the infinitely many unstable periodic orbits inside a chaotic attractor with vanishingly small parameter kicks. Here on the logistic map.

r: 3.900

Control starts at step: 80

Capture tolerance: 0.050

Apply OGY control after step 80

OGY chaos control (Ott-Grebogi-Yorke, 1990)

target: unstable fixed point  x* = 1 − 1/r = 0.7436

waiting phase: iterate freely until the trajectory enters
                the tolerance band |x − x*| < 0.050 around x*.

control kick:  pick δr such that f(x, r + δr) = x*, i.e.
                  δr  =  x* / (x (1 − x))  −  r

result: orbit is pinned to the previously-unstable
fixed point with arbitrarily small parameter perturbations.

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