Classical Dynamics of Particles and Systems · Problem 4-14

Gravitation — Marion & Thornton

Physics — Mechanics · chaos-divergence-30-percent

Problem

Use the function described in Example 4.3,

x_{n+1} = \alpha x_n(1 - x_n^2)

where

\alpha = 2.5

. Consider two starting values of

x_1

that are similar, 0.900 000 0 and 0.900 000 1. Make a plot of

x_n

versus

n

for the two starting values and determine the lowest value of

n

for which the two values diverge by more than 30\%.