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Subharmonic orbits in an anharmonic oscillator

Published online by Cambridge University Press:  17 February 2009

J. R. Christie ,
K. Gopalsamy  and
M. P. Panizza
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Abstract

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In a recent paper, Christie and Gopalsamy [2] used Melnikov's method to establish a sufficient condition for the existence of chaotic behaviour, in the sense of Smale, in a particular time-periodically perturbed planar autonomous system of ordinary differential equations. They then concluded with an application to the dynamics of a one-dimensional anharmonic oscillator. In this paper, the same system is considered and a condition for the existence of subharmonic orbits in the perturbed system is deduced, using the subharmonic Melnikov theory. Finally, an application is given to the dynamical behaviour of the one-dimensional anharmonic oscillator system.

Type
Research Article
Information
The ANZIAM Journal , Volume 38 , Issue 3 , January 1997 , pp. 307 - 315
Copyright
Copyright © Australian Mathematical Society 1997

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