×

zbMATH — the first resource for mathematics

Chaotic phenomena triggering the escape from a potential well. (English) Zbl 0674.70035
Summary: This paper explores the manner in which a driven mechanical oscillator escapes from the cubic potential well typical of a metastable system close to a fold. The aim is to show how the well-known atoms of dissipative dynamics (saddle-node folds, period-doubling flips, cascades to chaos, boundary crises, etc.) assemble to form molecules of overall response (hierarchies of cusps, incomplete Feigenbaum trees, etc.). Particular attention is given to the basin of attraction and the loss of engineering integrity that is triggered by a homoclinic tangle, the latter being accurately predicted by a Melnikov analysis. After escape, chaotic transients are shown to conform to recent scaling laws. Analytical constraints on the mapping eigenvalues are used to demonstrate that sequences of flips and folds commonly predicted by harmonic balance analysis are in fact physically inadmissible.

MSC:
70K50 Bifurcations and instability for nonlinear problems in mechanics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDF BibTeX XML Cite
Full Text: DOI