Combinatorial Resonances in a Coupled Duffing's Circuit with Asymmetry

Yue MA  Hiroshi KAWAKAMI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A    No.9    pp.2340-2346
Publication Date: 2003/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
coupled Duffing's circuits,  bifurcation,  combinatorial resonance,  

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A nonlinear circuit described by the forced Duffing's equation is known to display a rich variety of dynamical behavior. Coupling two Duffing's circuits by a linear resistor, we conclude that combinatorial resonances occur on weak coupling condition. In a coupled system, although symmetrical properties are usually observed, breaking of symmetry can lead to much more complex nonlinear resonant phenomena. In this paper, we discuss asymmetry in four cases of perturbation on parameters. Many bifurcation diagrams are presented. Comparing with symmetrical cases, we analyze the combinatorial resonances in coupled Duffing's circuit completely.