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Validating identified nonlinear models with chaotic dynamics. (English) Zbl 0876.58028

Summary: This paper investigates the effectiveness of several criteria for validating models which exhibit chaotic dynamics. Embedded trajectories, Poincaré 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 Poincaré 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.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
70K50 Bifurcations and instability for nonlinear problems in mechanics
37G99 Local and nonlocal bifurcation theory for dynamical systems
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