Footnotes:


Definition: Let be differentiable and let = , where is the eigenvalue of the DF matrix. It is the largest change in distance in all directions about , after the first n iterations. Then the Lyapunov number is given by,

~ Back

This shows that the Lyapunov exponent does not change with number of iterations. (Notice that the difference of the determent is so small. MatLab® was unable to resolve the difference) The negative sign indicates the attractor is in the period region. ~ Back

The right figure shows that the determent of the DF matrix does not change with number of iterations. (Notice that the difference of the determent is so small. MatLab® was unable to resolve the difference) The positive determent indicates the attractor is in the chaotic region. ~ Back