Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator | Zendy

Xueyong Wei | Zendy; Michel F. Randrianandrasana | Zendy; Mike Ward | Zendy; David Lowe | Zendy

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Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator

Author(s) -

Xueyong Wei,

Michel F. Randrianandrasana,

Mike Ward,

David Lowe

Publication year - 2010

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2011/248328

Subject(s) - van der pol oscillator , antiresonance , duffing equation , coupling (piping) , physics , resonator , nonlinear system , bifurcation , resonance (particle physics) , chaotic , symmetry breaking , symmetry (geometry) , synchronization (alternating current) , control theory (sociology) , quantum mechanics , mathematics , engineering , topology (electrical circuits) , computer science , optics , mechanical engineering , control (management) , artificial intelligence , combinatorics , geometry

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

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