May 1976 logistic map x_{n+1}=r·x_n·(1−x_n): period-doubling cascade

Layer 1 — Physicsin the complex-systems subtree

May 1976 (Nature 261:459) popularised the logistic difference equation as the minimal model of non-linear dynamics and chaos. Fixed points: x*=0 (unstable for r>1) and x*=1−1/r (stable for 1<r<3). Derivative at non-trivial fixed point:…

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First period-doubling bifurcation of logistic map at r=3 (|f'(x*)| = 1)

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