The logistic map is

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

The logistic map is xn+1=rxn(1−xn)x_{n+1} = r x_n (1-x_n). For r=2.2r = 2.2: (a) Compute the non-zero fixed point x∗=1−1/rx^* = 1 - 1/r to four decimal places, and check whether it attracts nearby points using ∣f′(x∗)∣=∣r(1−2x∗)∣<1|f'(x^*)| = |r(1-2x^*)| < 1. (b) Starting from x0=0.9x_0 = 0.9, iterate the map five times (x1,…,x5x_1,\dots,x_5) and report x5x_5 to four decimal places, confirming it lies close to x∗x^*.

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