Sensitivity to Initial Conditions in Chaos

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

While there is no agreement on a definition of chaos, sensitivity to initial conditions is usually considered an important marker. This Demonstration compares plots of a driven pendulum in a chaotic regime, started at two slightly different positions, to the same pendulum restricted to a regime of periodic orbits. The periodic regime varies the periodic driving force amplitude from 0.05 to 0.5 instead of from 0.1 to 1.0. The larger range includes a number of periodic orbits as well as chaotic ones.

Contributed by: Bruce Hawkins (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: quick coalescence to a periodic attractor

Snapshot 2: rapid divergence of trajectories in the chaotic regime

Snapshot 3: periodic attractor at a later time

Snapshot 4: trajectories can converge and diverge again; this is a period-two trajectory

The equation of motion is , with and .

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.