Abstract: Systems and methods for calculating the Lyapunov exponent of a chaotic system are described. In one particular embodiment, a Lyapunov exponent calculating method includes obtaining a value indicative of a condition of a chaotic system and assigning the value to first and second precision levels, the second precision level having a higher level of precision than the first precision level. The method also includes iterating the chaotic system over time and comparing the value at the first precision level with the value at the second precision level. From the comparison of values at the first and second precision levels, the method calculates the Lyapunov exponent for the chaotic system.

Abstract: Systems and methods for predicting the outcome of chaotic systems are described. An example of a prediction system disclosed herein includes, in general, functional elements to vary the initial conditions of a chaotic system and calculate a plurality of possible trajectories for the chaotic system. The prediction system also includes calculating a Lyapunov exponent for each of the plurality of possible trajectories and selecting the trajectory with the smallest Lyapunov exponent as the most likely trajectory to occur.