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Controlling transitions in a Duffing oscillator by sweeping parameters in time

Kogan, Oleg (2007) Controlling transitions in a Duffing oscillator by sweeping parameters in time. Physical Review E, 76 (3). Art. No. 037203. ISSN 1539-3755. doi:10.1103/PhysRevE.76.037203.

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We consider a high-Q Duffing oscillator in a weakly nonlinear regime with the driving frequency sigma varying in time between sigmai and sigmaf at a characteristic rate r. We found that the frequency sweep can cause controlled transitions between two stable states of the system. Moreover, these transitions are accomplished via a transient that lingers for a long time around the third, unstable fixed point of saddle type. We propose a simple explanation for this phenomenon, and find the transient lifetime to scale as −(ln|r−rc|)/lambdar, where rc is the critical rate necessary to induce a transition and lambdar is the repulsive eigenvalue of the saddle. Experimental implications are mentioned.

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Additional Information:©2007 The American Physical Society. (Received 13 November 2006; published 26 September 2007) The author thanks Professor Baruch Meerson for suggesting this problem and for subsequent discussions and Professor Michael Cross for pointing out the usefulness of thinking about the set {(f ,Yf)], as well as for general advice. We acknowledge the support of the PHYSBIO program with funds from the European Union and NATO as well as the NSF Grant No. DMR-0314069.
Subject Keywords:eigenvalues and eigenfunctions; nonlinear dynamical systems; oscillators; Q-factor
Issue or Number:3
Record Number:CaltechAUTHORS:KOGpre07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8926
Deposited By: Archive Administrator
Deposited On:01 Oct 2007
Last Modified:08 Nov 2021 20:54

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