Modeling nonlinear dynamics using multilayer neural networks

Certain deterministic nonlinear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analysed with linear techniques. However, uncovering the deterministic structure is important because it allows to construct more realistic and better models and thus improved predictive capabilities. The paper provides a new approach for features of chaotic systems definition. The proposed method includes a calculation of Lyapunov exponents using multilayer neural networks trained by a modified backpropagation error (BPE) algorithm. We compare the proposed technique and a widely used method for largest Lyapunov exponent definition for Henon and Lorenz chaotic processes.