Jr. Christie et al., SUBHARMONIC ORBITS IN AN ANHARMONIC-OSCILLATOR, Journal of the Australian Mathematical Society. Series B. Applied mathematics, 38, 1997, pp. 307-315
In a recent paper, Christie and Gopalsamy [2] used Melnikov's method t
o establish a sufficient condition for the existence of chaotic behavi
our, in the sense of Smale, in a particular time-periodically perturbe
d planar autonomous system of ordinary differential equations. They th
en concluded with an application to the dynamics of a one-dimensional
anharmonic oscillator. In this paper, the same system is considered an
d 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-dimensiona
l anharmonic oscillator system.