Symmetrical Properties and Bifurcations of the Periodic Solutions for a Hybridly Coupled Oscillator

Olivier PAPY

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E78-A    No.12    pp.1816-1821
Publication Date: 1995/12/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
symmetry,  bifurcation,  classification,  periodic solutions,  

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In this paper we study the bifurcations of the periodic solutions induced by the symmetrical properties of a system of hybridly coupled oscillators of the Rayleigh type. By analogy with the results concerning with the equilibria, we classify the periodic solutions according to their spatial and temporal symmetries. We discuss the possible bifurcations of each type of periodic solution. Finally we analyze the phase portraits of the system when the parameters vary.