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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Vibrational Resonance in the Duffing Oscillator with Distributed Time-Delayed Feedback

Journal of Applied Nonlinear Dynamics 4(4) (2015) 391--404 | DOI:10.5890/JAND.2015.11.006

C. Jeevarathinam$^{1}$; S. Rajasekar$^{1}$; M.A.F. Sanjuán$^{2}$

$^{1}$ School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India

$^{2}$ Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain

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Abstract

We analyze the vibrational resonance in the Duffing oscillator system in the presence of (i) a gamma distributed time-delayed feedback and (ii) integrative time-delayed (uniformly distributed time delays over a finite interval) feedback. Particularly, applying a theoretical procedure we obtain an expression for the response amplitude Q at the low-frequency of the driving biharmonic force. For both double-well potential and single-well potential cases we are able to identify the regions in parameter space where either (i) two resonances, (ii) a single resonance or (iii) no resonance occur. Theoretically predicted values of Q and the values of a control parameter at which resonance occurs are in good agreement with our numerical simulation. The analysis shows a strong influence of both types of time-delayed feedback on vibrational resonance.

Acknowledgments

CJ expresses his gratitude to University Grants Commission (U.G.C.), India for financial support in the form of U.G.C. meritorious fellowship. MAFS acknowledges financial support from the Spanish Ministry of Economy and Competitivity under Project No. FIS2013-40653-P.

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