if the Lyapunov exponent (L) = 0.9
and initial condition uncertainty = 0.1%
and we require that predictions of future behaviour in a system have errors less than or equal to 5%.
what is the time horizon (t) for making predictions?
I have been taught that t=(1/L)*ln(e/d(0)), where e=required accuracy of forecast, and d(0)=accuracy of initial measurement.
I'm assuming e=0.95, d(0)=0.99
Substituting what we have into the equation gives a negative value for t (t=-0.0559)
this seems wrong.
Am I using the formula correctly?
Any help would be appreciated!