At the logistic map settles onto a period-4 cycle

PHYSICS · Subjective · Fermi University Physics · Mechanics & Dynamical Systems · Nonlinear dynamics and chaos · Nonlinear dynamics and chaos

Computational Physics, Ch When trajectories separate: the driven pendulum and the logistic map

Problem

At r=3.5r = 3.5 the logistic map xn+1=rxn(1−xn)x_{n+1} = r x_n(1-x_n) settles onto a period-4 cycle. Starting from x0=0.1x_0 = 0.1, iterate the map for at least 6060 steps to let the transient die away, then read off the four values the iterate cycles through. Report them to four decimal places, listed in increasing order.

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