Combinatorial Resonances in Coupled Duffing's Circuits

Yue MA
Hiroshi KAWAKAMI

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A    No.3    pp.648-654
Publication Date: 2002/03/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
Keyword: 
coupled Duffing's circuits,  bifurcation,  combinatorial pattern,  

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Summary: 
In this paper, we study the fundamental combinatorial nonlinear resonances of a system consisting of two identical periodic forced circuits coupled by a linear resistor. The circuit equations are described by a system of coupled Duffing's equations. We discuss two cases of external periodic force, i.e., in-phase and anti-phase, and obtain the bifurcation diagram of each case. Periodic solutions are classified according to the symmetrical property of the circuit. Resonances in the coupled system are explained from the combinatorial standpoint. That is, we introduce the definition of combinatorial resonances and investigate the patterns of combinatorial solutions in this system.