Extended Methods for Calculating Largest Lyapunov Exponent from Small Data Sets

After analyzing recently common methods of calculating the largest Lyapunov exponent from small data sets, the irreversible property of time trajectories is studied and extended method for calculating the largest Lyapunov exponent of chaotic system is proposed based on backward or bi-direction search phase point. The computer simulation shows some valuable conclusions that the novel method is more anti-noise and precise that the old ones.