J Austral Math Soc Ser B 38 pp307--315, 1997.

Subharmonic orbits in an anharmonic oscillator

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

Abstract

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.

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Authors

J. R. Christie

K. Gopalsamy

M. P. Panizza

School of Information Science and Technology, The Flinders University of South Australia GPO Box 2100, Adelaide, SA, 5001 Australia.