Chapter

IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics

Volume 122 of the series Solid Mechanics and its Applications pp 69-78

Patterns of Bifurcation Suppressing Escape at Internal Resonance

  • G.H.M. van der HeijdenAffiliated withCentrefor Nonlinear Dynamics, University College London
  • , J.M.T. ThompsonAffiliated withCentrefor Nonlinear Dynamics, University College London

* Final gross prices may vary according to local VAT.

Get Access

Abstract

For an archetypal two-degree-of-freedom forced oscillator, relevant to a large class of mechanical problems, we examine the patterns of bifurcation that govem the internal 1:2 resonance of the system. A knowledge of these bifurcations allows the counter-intuitive suppression and control of escape by internal modal interactions. The bifurcations examined include symmetry-breaking pitchforks, Neimark bifurcations (secondary Hopf bifurcations) to a toroidal attractor, and chaotic crises which trigger dangerous large-amplitude excursions. We particularly focus on the effect that a symmetry-breaking imperfection has on the suppression of escape.

Key words

Suppression of escape 2 DOF forced oscillator symmetry breaking 1:2 resonance Neimark bifurcation unfolding