Estimating the lyapunov exponents of chaotic time series based on polynomial modelling

The problem of Lyapunov Exponents (LEs) estimation from chaotic data based on Jacobian approach by polynomial models is considered. The optimum embedding dimension of reconstructed attractor is interpreted as suitable order of model. Therefore, based on global polynomial mode ling of system, a novel criterion for selecting the embedding dimension is presented. By considering this dimension as the model order, the best nonlinearity degree of polynomial is estimated. The selected structure is used for local estimating of Jacobians to calculate the LEs. This suitable structure of polynomial model leads to better results and avoids of sporious LEs. Simulation results show the effectiveness of proposed methodology.