Chaotic Phenomena Triggering the Escape from a Potential Well

  • J. M. T. Thompson
Part of the International Centre for Mechanical Sciences book series (CISM, volume 319)


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.


Bifurcation Diagram Chaotic Attractor Homoclinic Orbit Harmonic Balance Basin Boundary 
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Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • J. M. T. Thompson
    • 1
  1. 1.University College LondonLondonUK

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