Nonlinear Local Lyapunov Exponent and Quantification of Local Predictability

Nonlinear local Lyapunov exponent (NLLE) is applied to quantitatively determine the local predictability limit of chaotic systems. As an example, we find that the local predictability limit of Henon attractor varies considerably with time, and some underlying phase-spatial structure does not appear. The local predictability limit of initially adjacent points in phase space may be completely different. This will cause difficulties in making the long-time analogue forecast.