Validating Identified Nonlinear Models with Chaotic Dynamics

This paper investigates the effectiveness of several criteria for validating models which exhibit chaotic dynamics. Trajectories in the pseudo-phase-plane, Poincare sections, bifurcation diagrams,the largest Lyapunov exponent and correlation dimension are considered. The Duffing-Ueda equation and four identified models are used as examples. The results show that models with similar invariants such as Poincare sections, the largest Lyapunov exponent and correlation dimension may have very different bifurcation behaviours. This suggests that the requirement that an identified model should reproduce the bifurcation pattern of the original system is a very exacting criterion which is well suited for validation purposes.