The Lorenz Model - Demo 8

Sensitive Dependence on Initial Conditions

What happens if we start out the evolution first from one initial condition, and then from one that differs by a small amount, and compare the two orbits? We can do this by plotting both trajectories simultaneously on the same plot, first the X-Z projection of the phase space trajectory:

and then directly in the X(t) plot:

The two orbits track each other for a considerable time, but even after a quite short time, are behaving quite differently.

This is the basic conclusion of Lorenz's work: even if you know the initial conditions quite precisely the error in specifying the initial condition rapidly grows, so that after even a short time we cannot predict the details of the motion - the sensitive dependence on initial conditions that is one of the defining properties of chaos.

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Last modified Thursday, January 6, 2000
Michael Cross