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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Vibrational Resonance in a System with a Signum Nonlinearity

Discontinuity, Nonlinearity, and Complexity 5(1) (2016) 43--58 | DOI:10.5890/DNC.2016.03.006

K. Abirami$^{1}$, S. Rajasekar$^{1}$, M.A.F. Sanjuan$^{2}$

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

$^{2}$ Departamento de F´ısica, Universidad Rey Juan Carlos, Tulipán s/n, 28933 M´ostoles, Madrid, Spain

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We present our investigation on vibrational resonance in a system with a signum nonlinearity. We construct an exact analytical solution of the system in the presence of an external biharmonic force with two frequencies ω and Ω, Ω≥ω and use it for the computation of the response amplitude Q at the low-frequency ω. We analyse the effect of the strength of the signum nonlinearity on vibrational resonance for the cases of the potential with a single-well, a double-well and a single-well with a double-hump. An interesting feature of vibrational resonance in the system is that Q does not decay to zero for g (the amplitude of the high-frequency force) → ꝏ. We compare the features of the vibrational resonance of these two systems, since the potential of the system with the signum nonlinearity and that of the Duffing oscillator show ssimilar forms. The strength of the nonlinearity in these two systems is found to give rise distinct effects on resonance.


KA acknowledges the support from University Grants Commission (UGC), India in the form of UGC-Rajiv Gandhi National Fellowship. MAFS acknowledges financial support from the Spanish Ministry of Economy and Competitiveness under Project No. FIS2013-40653-P.


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