Forecasting Silicon content in hot metal of blast furnace based on Lyapunov exponents;

Chaos characteristics of electrode displacement signals in spot welding process based on Lyapunov exponent;

Lyapunov exponent of chaos feature in the processing of deformation failure for coal floor;

Early detecting of fault arcs using Lyapunov exponents;

Analysis of Lyapunov exponents in class of nonlinear electrical oscillator;

Computing Lyapunov exponents with feedforward neural networks;

Simulation research on chaos state in traffic flow based on the maximum Lyapunov index;

Cost predicting method on improved largest Lyapunov index;

Lyapunov index and time scale of predictability in phase space;

A software was exploited for computing spectrum of Lyapunov exponents in chaotic dynamic system.

Moreover, the method for calculating the spectrum of Lyapunov exponents of the impact-vibrating system is obtained.

Visual inspection and the positive Lyapunov exponent suggest the chaotic na- ture.

In this paper, studies to electric load time series shows that the time series is not random series but chaotic ones, by calculating the chaotic character exponents: the largest Lyapunov exponent and correlation dimension.

The analysis of Lyapunov exponents and bifurcation diagram demonstrates evolution process from hyperchaos,chaos,quasi-periodic orbits and periodic orbits as the parameter increases.