Journal of Applied Nonlinear Dynamics
Vibrational Resonance in the Duffing Oscillator with Distributed TimeDelayed Feedback
Journal of Applied Nonlinear Dynamics 4(4) (2015) 391404  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 timedelayed feedback and (ii) integrative timedelayed (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 lowfrequency of the driving biharmonic force. For both doublewell potential and singlewell 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 timedelayed 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. FIS201340653P.
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