Patterns of Bifurcation Suppressing Escape at Internal Resonance
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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.
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- Patterns of Bifurcation Suppressing Escape at Internal Resonance
- Book Title
- IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics
- Book Subtitle
- Proceedings of the IUTAM Symposium held in Rome, Italy, 8–13 June 2003
- Book Part
- pp 69-78
- Print ISBN
- Online ISBN
- Series Title
- Solid Mechanics and its Applications
- Series Volume
- Series ISSN
- Springer Netherlands
- Copyright Holder
- Additional Links
- Suppression of escape
- 2 DOF forced oscillator
- symmetry breaking
- 1:2 resonance
- Neimark bifurcation
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