Logistic Map Cobweb

x_{n+1} = rx_n(1-x_n) — period doubling cascade to chaos, Lyapunov exponents, bifurcation diagram

r (growth rate)3.500

Iterations150

Cobweb speed8

Bifurc resolution300

Period doubling: r=3→period 2, r≈3.449→period 4, r≈3.544→period 8… Feigenbaum constant δ≈4.669. At r≈3.57: chaos onset. r≈3.83: period-3 window (Li-Yorke: period 3 implies chaos).