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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 a Duffing System with a Generalized Delayed Feedback

Journal of Applied Nonlinear Dynamics 2(4) (2013) 397--408 | DOI:10.5890/JAND.2013.11.006

J.H. Yang$^{1}$; Miguel A.F. Sanjuán$^{2}$; C.J.Wang$^{3}$; H. Zhu$^{1}$

$^{1}$ School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, P.R. China

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

$^{3}$ Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721016, P.R. China

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Abstract

We investigate the vibrational resonance in the Duffing system with different kinds of delayed feedback. Our approach is to consider the delayed feedback as a generalized delayed feedback in a fractional-order differential version. For three special cases, the generalized delayed feedback corresponds to displacement delayed feedback, velocity delayed feedback, and acceleration delayed feedback respectively. At first, based on the vibrational mechanism, the approximate solution of the system is obtained. Then, we give conditions for all resonance patterns. The the oretical predictions are verified by numerical simulations. Furthermore, the theoretical results are in good agreement with the numerical simulations. Since the delayed feedback is in a generalized form, our results can be regarded as universal for the vibrational resonance in nonlinear systems with different kinds of delayed feedback.

Acknowledgments

We acknowledge financial support from the China Postdoctoral Science Foundation (Grant No.2012M510192), Qihang Plan of China University of Mining and Technology (CUMT), Scientific Research Foundation for Talents Introduced into CUMT (Grant No. 2011RC13), the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the Spanish Ministry of Science and Innovation (Grant No. FIS2009-09898).

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