Discrete Reconstruction of the Double Scroll Attractor

This work is concerned with the discrete reconstruction of the double scroll attractor. Two aspects of the reconstruction are investigated,a, the discretization of the original equations via numerical methods and b, the identification of of discrete nonlinear models from time series generated by the original system. The quality of the model is assessed by estimating the largest Lyapunov exponent, the correlation dimension and by comparing the geometry of the reconstructed attractor to the original double scroll. The major aim of the paper is to investigate how parameters such as the discretization period, sampling rate and the number of terms in an estimated model affect the dynamics and also to point out if there is any relationship among such parameters. Conclusions in this direction are believed to be especially relevant in determining adequate model structures in identification applications. This is known to be critical in the identification of nonlinear systems.