Jumps to Resonance: Long Chaotic Transients, Unpredictable Outcome, and the Probability of Restabilization

[+] Author and Article Information
M. S. Soliman

Department of Civil Engineering, University College London, London, WC1E 6BT, U.K.

J. Appl. Mech 60(3), 669-676 (Sep 01, 1993) (8 pages) doi:10.1115/1.2900856 History: Received July 18, 1991; Revised January 07, 1992; Online March 31, 2008


For nonlinear oscillators with the ability to escape from a potential well, jumps to resonance from a fold can result in qualitatively different types of response. They may be safe where the system always restabilizes onto a oscillation within the well; unsafe where the system always escapes out of the well; or indeterminate where the outcome is unpredictable. In the indeterminate case, long chaotic transients may persist before the system decides to which long-term behavior it will settle upon. We determine at which control parameters indeterminate jumps occur. We also examine how the transients scale as well as the probability of restabilization after the bifurcation.

Copyright © 1993 by The American Society of Mechanical Engineers
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