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2009•Acta Physica SinicaOpen access

Bifurcation analysis of a compound oscillator with parametric and external excitation

Ji Ying, Bi Qin-Sheng, 江苏大学理学院，镇江 212013

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Abstract

The dynamics of a compound oscillator with parametric and external excitation has been investigated. Local bifurcation analysis of the first order approximation shows that simple bifurcation as well as Hopf bifurcation may take place，as have been observed in the original system. The influence of several parameters on the dynamics has been explored，which reveals that different nonlinear behaviors can be obtained with the variation of the parameters. Furthermore，by employing global bifurcation theory，the necessary conditions for homoclinic and heteroclinic bifurcation has been presented，which agrees well with the numerical results.

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What this paper is about

The dynamics of a compound oscillator with parametric and external excitation has been investigated. Local bifurcation analysis of the first order approximation shows that simple bifurcation as well as Hopf bifurcation may take place，as have been observed in the original system. The influence of several parameters on the dynamics has been explored，which reveals that different nonlinear behaviors can be obtained with the variation of the parameters. Furthermore，by employing global bifurcation theory，the necessary conditions for homoclinic and heteroclinic bifurcation has been presented，which agrees well with the numerical results.

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Available abstract

The dynamics of a compound oscillator with parametric and external excitation has been investigated. Local bifurcation analysis of the first order approximation shows that simple bifurcation as well as Hopf bifurcation may take place，as have been observed in the original system. The influence of several parameters on the dynamics has been explored，which reveals that different nonlinear behaviors can be obtained with the variation of the parameters. Furthermore，by employing global bifurcation theory，the necessary conditions for homoclinic and heteroclinic bifurcation has been presented，which agrees well with the numerical results.

Key concepts: Homoclinic bifurcation, Biological applications of bifurcation theory, Bifurcation, Heteroclinic bifurcation, Transcritical bifurcation, Saddle-node bifurcation, Parametric statistics, Pitchfork bifurcation

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