Jr. Christie et K. Gopalsamy, CHAOS IN AN ANHARMONIC-OSCILLATOR, Journal of the Australian Mathematical Society. Series B. Applied mathematics, 37, 1995, pp. 186-207
Using Melnikov's method, the existence of chaotic behaviour in the sen
se of Smale in a particular time-periodically perturbed planar autonom
ous system of ordinary differential equations is established. Examples
of planar autonomous differential systems with homoclinic orbits are
provided, and an application to the dynamics of a one-dimensional anha
rmonic oscillator is given.