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Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator
Joint Authors
Ward, M.
Wei, X.
Lowe, D.
Randrianandrasana, M. F.
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-10-04
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling.
Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours.
A two-time scales method is used to obtain the frequency-amplitude modulation.
The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator.
The stability of the dynamic motions is also analyzed.
The coupled system shows a hysteretic response pattern and symmetry-breaking facets.
Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.
American Psychological Association (APA)
Wei, X.& Randrianandrasana, M. F.& Ward, M.& Lowe, D.. 2010. Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-457184
Modern Language Association (MLA)
Wei, X.…[et al.]. Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator. Mathematical Problems in Engineering No. 2011 (2011), pp.1-16.
https://search.emarefa.net/detail/BIM-457184
American Medical Association (AMA)
Wei, X.& Randrianandrasana, M. F.& Ward, M.& Lowe, D.. Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator. Mathematical Problems in Engineering. 2010. Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-457184
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-457184