Estimating the LLE Based on Predicting Chaotic Time Series

It is usually hard to calculate Lyapunov exponent of a system or a time series exactly. For a chaotic system, the largest Lyapunov exponent (LLE) is positive. So estimating the largest Lyapunov exponent is an important for a nonlinear system. In this paper, the problems of LEs of difference differential dynamic system are discussed. An algorithm for estimating the largest Lyapunov exponent is developed by combining the predicting chaotic time series and modified matrix method for calculating Lyapunov exponents. This novel algorithm can avoid solving the optimization problem and reducing the workload of related computations. The algorithm can be employed to predict the largest Lyapunov exponent to see the system is stable or not