Then a method is introduced,where Lyapunov exponent is calculated by formula for a single neuron,and small-data algorithm is used to obtain the largest Lyapunov exponent for the neural network composed of neurons.

The small-data method is improved by false nearest neighbor method calculating embedding dimension.

But the improved small-data method may lead to false identification of chaos.

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.

First,the improved algorithm uses correlation integral method(C-C method) and Cao method to estimate two important variances of phase space reconstruction: embedding dimension m and delay time,then,uses small data sets to calculate the largest Lyapunov exponent from the time series.

Empirical study on chaotic attractor in stock market based on G-P arithmetic and small data arithmetic;

The differences between them lies their grammatical positions which are complementary,and both structures have the same meaning of "small amount" and possess the characteristics of the jargon of Zen Buddhism.